" LIBRARY OF CONGRESS. 

%p..^T^ttp^i9]^ :fu 

UNITED STATES OF AMERICA. 



ELEMENTS 




SURVEYING, 



NAVIGATION, 

WITH DESCRIPTIONS OF THE INSTRUMENTS AND THE 
NECESSARY TABLES. 

BY CHAELES DAVIES, LL. D., 

AUTHOR OF ARITHMETIC, ALGEBRA, PRACTICAL MATHEMATICS FOR PRACTICAL MEN, 

ELEMENTS OF DESCRIPTIVE GEOMETRY, SHADES, SHADOWS, AND PER- 

SPECTITE, ANALYTICAL GEOMETRY, DIFFERENTIAL AND 

INTEGRAL CALCULUS. 



REVISED EDITION. 




NEW YOEK: 

PUBLISHED BY A. S. BARNES & CO., 

No. 51 JOHN-STREET. 

CINCINNATI: H. W. DERBY & CO., 

1851. 



/. 

^ 



DA VIE S' 
COURSE OF MATHEMATICS 



IBabies* iFivst Wessons in ^tiQmetic— For Beginners. 

Jiabies' ^ritjmetic— Designed for the use of Academies and Schools. 

I&ej to 3Bai)ics' 'Mtititmetic. 

Jiabies' Sanfbersitj ^ritt)mctic — Embracing the Science of Numbers and their 
numerous Applications. 

Ites to IBabies* sanibnsitj ^ritljmetic. 

3iabies* IBlcmcntarw Sllficljra — Being an introduction to the Science, and form- 
ing a connecting hnk between Arithmetic and Algebra. 

2&£2 to Babies' SElementnvs ^laefira. 

IBabiES' 3Slemcnts of ©EomettD and STrigonometrj, with Applications in 
Mensuration. — This work embraces the elementary principles of Geometry and 
Trigonometry. The reasoning is plain and concise, but at the same time strictly 
rigorous. 

Babies' 33'^actical lEatijematfcs for 33tractical iHSen — Embracing the Princi- 
ples of Drawing, Arcliitecture, Mensuration, and Logarithms, with Applications 
to the Mechanic Arts. 

Babies' 3Souraon's Algebra — Including Sturm's Theorem — Being an abridg- 
ment of the Work of M. Bourdon, with the addition of practical examples. 

Babies' Hcgcntrre's ©feometrj and SCrigonometrs — From the works of A. M. 
Legendre, with the addition of a Treatise on Mensuration of Planes and 
Solids, and a Table of Logarithms and Logarithmic Sines. 

Babies' Surbejing — With a description and plates of the Theodolite, Com- 
pass, Plane-Table, and Level ; also, Maps of the Topographical Signs adopted 
by the Engineer Department — an explanation of the method of surveying the 
Public Lands, Geodesic and Maritime Surveying, and an Elementary Treatise 
on Navigation. 

Babies' Bescriptibc CKeometrB — With its application to Spherical Projec- 
tions. 

Babies' S|)atres, Sljattotos, and llijteai? 33ei^sj)ectibe. 

Babies' ^nalstical fiSeometrj — Enjbi'acing the Equations of the Point and 
Straight Line — of the Oonio Sections — of the Line and Plane in Space ; 
also, the discussion of the General Equation of the second degree, and of Sub- 
faces of the second order. 

Babies' Btfferential and integral Calculus. 



5 



Entered according to Act of Congress, in the year one thousand eight hundred and 
(^ fifty-one, by Charles Davies, in the Clerk's Office of the District Court of the 
^ United States for the Southern District of New York. 

J. p. JONES & CO., Stkbeoiypees. F. C. GUTIERBEZ, Pbimtee. 



S-3^7?/ 



PREFACE 



The Elements of Surveying, first publislied in 1830, 
was designed as a text-book for tlie pupils of the Military 
Academy, and in its preparation little regard was liad to 
the supposed wants of other institutions. 

The work, however, was received by the public with 
more favor than was anticipated, and soon became a lead- 
ing text-book in the Colleges, the Academies, and the 
higher grade of Schools. 

For the purpose of adapting it, more fully, to the sup- 
posed wants of these institutions many changes have been 
made, since its first publication, and the present edition 
will be found to differ, in many respects, from those which 
have preceded. 

It has been the intention to begin with the very ele- 
ments of the subject, and to combine those elements in 
the simplest manner, so as to render the higher branches 
of plane surveying comparatively easy. All the instru- 
ments needed for plotting have been carefully described ; 
and the uses of those required for the measurement of 
angles are fully explained. 

The conventional signs adopted by the Topographical 
Bureau, which are now used by the United States Engi- 
neers in all their Charts and Maps, are given in plates 
5 and 6. 

Should these signs be generally adopted in the country, 
it would give entire uniformity to all maps and delinea- 
tions of the ground, and would establish a kind of lan- 
guage by which all the peculiarities of soil and surface 
could be accurately represented. 



IV PREFACE. 

A section lias also been added on Geodesy. This 
branch of Surveying is extensively applied in the Coast 
Survey, and now forms an important element of a practi- 
cal or scientific education. 

A full account is also given of the manner of survey- 
ing the public lands; and, although the method is simple, 
it has, nevertheless, been productive of great results, by 
defining, with mathematical precision, the boundaries of 
lands in the new States, and thus settling their titles on 
an indisputable basis. 

This method was originated by Col. Jared Mansfield, 
whose great acquirements in science introduced him to the 
notice of President Jefferson, by whom he was appointed 
surveyor- general of the North-Western Territory. 

May it be permitted to one of his pupils, and a gradu- 
ate of the Military Academy, further to add, that at the 
organization of the institution in 1812, he was appointed 
Professor of Natural and Experimental Philosophy. This 
situation he filled for sixteen years, when he withdrew 
from the Academy to spend the evening of his life in re- 
tirement and study. His pupils, who had listened to his 
instructions with delight, who honored his learning and 
wisdom, and had been brought near to him by his i^ind 
and simple manners, have placed his portrait in the public 
library, that the institution might possess an enduring 
memorial of one of its brightest ornaments and distin- 
guished benefactors. 

At the solicitation of several distinguished teachers, there 
is added, in the present edition, an article on Plane Sail- 
ing, most of which has been taken, by permission of the 
author, from an excellent work on Trigonometry and its 
applications, by Professor Charles W. Hackley. 

FiSHKiLL Landing, 
July, 1851. 



CONTENTS. 



BOOK I. 

SECTION I. 

PAGE. 

Of Logarithms, 9 

Table of Logarithms, 11 

Multiplication by Logarithms,. 15 

Division by Logarithms, '. ^ _ 16 

Arithmetical Complement, 17 

SECTION IX. 

Geometrical Definitions, 19 

Geometrical Constructions, 25 

Description of Instruments, 25 

Dividers, 25 

Ruler and Triangle, 25 

Scale of Equal Parts, 27 

Diagonal Scale of Equal Parts, 27 

Scale of Chords, 29 

Semicircular Protractor, •_... 30 

Sectoral Scale of Equal Parts, 30 

Gunter's Scale, 32 

Solution of Problems, 32 

SECTION III. 

Plane Trigonometry, 38 

Division of the Circumference, 38 

Definitions of the Trigonometrical Lines, 39 

Table of Natural Sines, 40 

Table of Logarithmic Sines, 41 

Theorems, 44 

Solution of Triangles, 48 

Solution of Right-Angled Triangles, , 54 

Application to Heights and Distances, 55 



VI CON-TENTS. 

BOOK II. 
PLANE SURVEYING. 

SECTION I. 

PAGE. 

Definitions, 64 

Measurement of Lines and Angles, 66 

Measures for Distances, 66 

To Measure a Horizontal Line, 67 

Measurement of Angles, 69 

Of the Theodolite, 69 

Verniers, 75 

To Measure a Horizontal Angle with the Theodolite, 77 

To Measure a Vertical Angle, 78 

Measurements with the Tape or Chain, 79 

Surveying Cross, 81 

SECTION II. 

Area, or Contents of Ground, , 85 

Of Laying out Land, 96 

SECTION III. 

The Circumferenter, or Surveyor's Compass, 98 

Surveying with the Compass, Definitions, etc., 99 

Field Operations, 103 

Traverse Table, 105 

Of Balancing the Work, 109 

Of the Double Meridian Distances of the Courses, 113 

Of Finding the Area, 114 

First Method of Plotting, 117 

Second Method of Plotting, 117 

Problems, 118 

Offsets, 123 

Of Supplying Omissions in the Field Notes, 124 

To Determine the Angle between two Courses, ■. 186 

Of Dividing Land, 127 

SECTION IV. 

Method of Surveying the Public Lands, 131 

Variation of the Needle, 134 

Method of Ascertaining the Variations, 138 

To Find the True Meridian with the Theodolite, 140 

To Find the True Meridian with the Compass, 141 



CONTENTS. Vli 

BOOK III. 
LEVELLING AND TOPOGRAPHICAL SURVEYING. 

SECTION I. 

PAGE. 

Of Levelling, 145 

The Y Level, 147 

The Water Level, ., 150 

Levelling Staves, 151 

Levelling in the Field, 153 

Difference of Level between Tw^o Points, 153 

Example, 154 

Levelling for Section, 157 

Plotting the Section or Profile, 158 

SECTION II. 

Topographical Surveying, 159 

Field Notes, 166 

Plotting the Work, 167 

BOOK lY. 

GEODESIC, TRIGONOMETRIC, AND MARITIME 
SURVEYING. 

SECTION I. 

Geodesic and Trigonometric Surveying, 173 

Preliminary Reconnoissance and Establishment of Signals, 174 

Measurement of a Base Line, 176 

Triangulation, 178 

Filling up the Survey, 181 

Use of the Compass, 181 

The Plane Table— Its Uses, 183 

To Measure a Horizontal Angle, 185 

To Determine Lines in Extent and Position, 185 

Of Changing the Paper, 187 

Reduction to the Centre,. 189 

Spherical Excess, 190 

Plotting the Triangulation, 192 

The Circular Protractor, 192 

To Lay off an Angle with the Protractor, 193 

First Method of Plotting, 193 

Second Method of Plotting, 194 

Method of Chords, 195 

To Layoff an Angle, 196 

SECTION II. 

Maritime Surveying, '. 197 



Vlll COITTENTS. 

BOOK V. 
OF NAVIGATION. 

SECTION I, 

PAGE. 

Definitions, 201 

SECTION II. 

Of Plane Sailing, 205 

SECTION III. 

Of Traverse Sailing, 207 

Of Plotting, 209 

SECTION IV. 

Parallel Sailing, 211 



Middle Latitude Sailing, 214 

Mercator's Sailing,. . '. 218 

Mercator's Chart, 221 

Line of Meridional Parts on Gunter's Scale, 222 



ELEMENTS OP SURYEYMG. 



BOOK I. 

SECTION I. 

OF LOGAEITHMS. 

1. The logarithm of a number is the exponent of the power 
to which it is necessary to raise a fixed number^ in order to 
produce the first number. 

TMs fixed number is called tlie base of tlie system, and 
may be any number except 1 : in tlie common system, 10 
is assumed as tlie base. 

2. If we form tbose powers of 10, wHcli are denoted 
by entire exponents, we shall have 

10" =1 10' = 10, 10' = 1000 

10' = 100, 10^ = 10000, &c., &c.. 

From tbe above table, it is plain, tbat 0, 1, 2, 8, 4, &c., 
are respectively the logarithms of 1, 10, 100, 1000, 10000, 
&c. ; we also see, tbat the logarithm of any number be- 
tween 1 and 10, is greater than and less than 1 : thus, 
log 2 = 0.301030. 

The logarithm of any number greater than 10, and less 
than 100. is greater than 1 and less than 2 : thus, 
log 50 = 1.698970. 

The logarithm of any number greater than 100, and 
less than 1000, is greater than 2 and less than 3 : thus, 



10 ELEMENTS OF SURVEYING. [BOOK I. 

If tlie above principles be extended to otber numbers, 
it will appear, tbat the logarithm of any number, not an 
exact power of ten, is made up of two parts, an entire and 
a decimal part. The entire part is called the characteristic 
of the logarithm^ and is always one less than the number of 
places of figures in the given number. 

3. The principal use of logarithms, is to abridge nu- 
merical computations. 

Let M denote any number, and let its logarithm be 
denoted by m ; also let N denote a second number whose 
logarithm is w; then, from the definition, we shall have, . 

10"" = if (1) 10" = iV(2). 

Multiplying equations (1) and (2), member by member, 
we have, 

10"' + " = MX N or, m + n=\og {MxN); hence. 

The sum of the logarithms of any two numbers is equal to 
the logarithm of their product. 

4. Dividing equation (1) by equation (2), member by 
member, we have, 

m-n ^ ^^ 

10 = j;t or, m — n = log -Tf- hence, 

The logarithm of the quotient of two numbers, is equal to 
the logarithm of the dividend diminished by the logarithm of 
the divisor. 

5. Since the logarithm of 10 is 1, the logarithm of the 
product of any number by 10, will be greater by 1 than the 
logarithm of that number ; also, the logarithm of the quotient 
of any number divided by 10, will be less by 1 than the 
logarithm of that number. 

Similarly, it may be shown that if any number be mul- 
tiplied by one hundred, the logarithm of the product will 
be greater by 2 than the logarithm of that number ; and 
if any number be divided by one hundred, the logarithm 
of the quotient will be less by 2 than the logarithm of. 
that number, and so on. 



SEC, I] LOGARITHMS. 11 

EXAMPLES, 

log 327 is 2.514548 

log 32.7 " 1.514548 

. log 3.27 " 0.514548 

log .327 " 1.514548 

log .0327 " 2.514548 

From tlie above examples, we see, tliat in a number 
composed of an entire and decimal part, we may cbange 
the place of tlie decimal point without changing the deci- 
mal part of the logarithm; but the characteristic is dimin- 
ished by 1 for every place that the decimal point is removed to 
the left. 

In the logarithm of a decimal, the characteristic becomes 
negative, and is numerically 1 greater than the number of 
ciphers immediately after the decimal point. The negative 
sign extends only to the characteristic, and is written over 
it, as in the examples given above. 

TABLE OP LOGARITHMS. 

6. A table of logarithms, is a table in which are writ- 
ten the logarithms of all numbers between 1 and some 
given number. The logarithms of all numbers between 1 
and 10,000 are given in the annexed table. Since rules 
have been given for determining the characteristics of 
logarithms by simple inspection, it has not been deemed 
necessary to write them in the table, the decimal part 
only being given. The characteristic, however, is given 
for all numbers less than 100. 

The left hand column of each page of the table, is the 
column of numbers, and is designated by the letter N; 
the logarithms of these numbers are placed opposite them 
on the same horizontal line. The last column on each 
page, headed D, shows the difference between the loga- 
rithms of two consecutive numbers. This difference is 
found by subtracting the logarithm under the column 
headed 4, from the one in the column headed 5 in the 
same horizontal line, and is nearly a mean of the differ- 
ences of any two consecutive logarithms on this line. 



d^ 



12 ELEMENTS OF SURVEYING. [BOOK I. 

To find^ from the table, the logarithm of any number. 

7. If the number is less than 100, look on tlie first page 
of the table, in the column of numbers under N, until the 
number is found: the number opposite is the logarithm 

ought : ThuSj 

log 9 = 0.954243. 

When the number is greater than 100 and less than 1000. 

8. Find in the column of numbers, the first three figures 
of the given number. Then pass across the page along a 
horizontal line until you come into the column under the 
fourth figure of the given number : at this place, there are 
four figures of the required logarithm, to which two figures 
taken from the column marked 0, are to be prefixed. 

If the four figures already found stand opposite a row 
of six figures in the column marked 0, the two left hand 
figures of the six, are the two to be prefixed ; but if they 
stand opposite a row of only four figures, you ascend the 
column till you find a row of six figures ; the two left 
hand figures of this row are the two to be prefixed. If 
you prefix to the decimal part thus found, the character- 
istic, you will have the logarithm sought: Thus, 

log 8979 = 3.953228 
log .08979 = 2.953228 

If, however, in passing back from the four figures found, 
to the column, any dots be met with, the two figures 
to be prefixed must be taken from the horizontal line di- 
rectly below : Thus, 

log 3098 = 3.491081 
log 30.98 = 1.491081 

If the logarithm falls at a place where the dots occur, 
must be written for each dot, and the two figures to be 
prefixed are, as before, taken from the line below: Thus, 

log 2188 = 3.340047 
log .2188 = 1.340047 



SEC. L] LOGARITHMS. 13 

When the number exceeds 10,000. 

9. The characteristic is determined by the rules already 
given. To find the decimal part of the logarithm : place 
a decimal point after the fourth figure from the left 
hand, converting the given number into a whole number 
and decimal. Find th^ logarithm of the entire part by the 
rule just given, then take from the right hand column of 
the page, under D, the number on the same horizontal 
line with the logarithm, and multiply it by the decimal 
part; add the product thus obtained to the logarithm al- 
ready found, and the sum will be the logarithm sought. 

If, in multiplying the number taken from the column 
Jj{, the 4^1^9.1 * part of the product exceeds .5, let 1 be 
added to the entire part; if it is less than .5, the decimal 
part of the product is neglected. 

EXAMPLE. 

I 

1. To find the logarithm- of the number 672887. 

The characteristic is 5. ; placing a decimal point after 
the fourth figure from the; left, we have 6728.87. The 
decimal part' of the 'log'* 6728 is .827886', and the corres- 
ponding number in the column D is 65'; 'then 65x.87= 
66.55, ' and since the decimal part exceeds ^ .5, we have 57 
to be added to .827886, which gives .827943. 

Hence, log 672887 = 5.827943 

Similarly, log .0672887 = 2.827943 

The last rule has been deduced under the supposition 
that the difference of the numbers is proportional to the 
difference of their logarithms, which is suf&ciently exact 
within the narrow limits considered. 

In the above example, 65 is the difference between the 
logarithm of 672900 and the logarithm of 672800, that is, 
it is the difference between the logarithms of two numbers 
which differ by 100. 

We have then the proportion 

100 : 87 : : 65 : 56.55, 

hence, 56.55 is the number to be added to the logarithm 
before found. 



14 ELEMENTS OF SURVEYlNa. [BOOK I. 

To find from, the table the nwriber corresponding to a given 
logarithm. 

10. Search, in tlie columns of logarithms for the decimal 
part of the given logarithm : if it cannot be found in the 
table, take out the number corresponding to the next less 
logarithm and set it aside. Subtract this less logarithm 
from the given logarithm, and annex to the remainder as 
many zeros as may be necessary, and divide this result by 
the corresponding number taken from the column marked 
D, continuing the division as long as desirable : annex the 
quotient to the number set aside. Point off, from the left 
hand, as many integer figures as there are units in the 
characteristic of the given logarithm increased by 1; the 
result is the required number. 

If the characteristic is negative, the number will be 
entirely decimal, and the number of zeros to be placed at 
the left of the number found from the table, will be equal to 
th,3 number of units in the characteristic diminished by 1. 

This rule, like its converse, is founded on the supposi- 
tion that the difference of the logarithms is proportional 
to the difference of their numbers within narrow limits. 

EXAMPLE. 

1. Find the number corresponding to the logarithm 
8.233568. 

The decimal part of the given logarithm is .233568 
The next less logarithm of the table is .233504, 

and its corresponding number 1712. 

Their difference is - - - - 64 

Tabular difference 253)6400000(25 

Hence, the number sought 1712.25. 

The number corresponding to the logarithm 3.233568 

is .00171225. 

2. What is the number corresponding to the logarithm 
2.785407? Ans. .06101084. 

3. What is the number corresponding to the logarithm 
1.846741? Aois. .702653. 



SEC. I.] LOGARITHMS. 15 

MULTIPLICATIOIf BY LOGAEITHMS. 

11. Wten it is required to multiply numbers by means 
of their logarithms, we first find from the table the loga- 
rithms of the numbers to be multiplied; we next add 
these logarithms together, and their sum is the logarithm 
of the product of the numbers (Art. 3). 

The term sum is to be understood in its algebraic 
sense; therefore, if any of the logarithms have negative 
characteristics, the difference between their sum and that 
of the positive characteristics, is to be taken ; the sign of 
the remainder is that of the greater sum. 

EXAMPLES. 

1. Multiply 23.14 by 5.062. 

log 23.14 = 1.364363 
log 5.062 = 0.704322 

Product, 117.1347 . . . 2.068685 



2. Multiply 3.902, 597.16, and 0.0314728 together. 

log 3.902 = 0.591287 

log 597.16 = 2.776091 
log 0.0314728 = 2.497936 

Product, 73.3354 .... 1.865314 



Here, the 2 cancels the + 2, and the 1 carried from 
the decimal part is set down. 

3. Multiply 3.586, 2.1046, 0.8372, and 0.0294 together. 

log 3.586 = 0.554610 
log 2.1046 = 0.323170 
log 0.8372 = 1.922829 
log 0.0294 = ^.468347 

Product, 0.1857615 . . 1.268956 

In this example the 2, carried from the decimal part, 
cancels 2, and there remains 1 to be set down. 



16 ELEMENTS OF SURVEYINGf. [BOOK I. 

DIVISION OF JSrUMBEES BY LOGARITHMS. 

12. When it is required to divide numbers by means 
of their logarithms, we have only to recollect, that the 
subtraction of logarithms corresponds to the division of 
their numbers (Art. 4). Hence, if we find the logarithm 
of the dividend, and from it subtract the logarithm of the 
divisor, the remainder will be the logarithm of the quotient. 

This additional caution may be added. The difference 
of the logarithms, as here used, means the algebraic differ- 
ence ; so that, if the logarithm of the divisor have a nega- 
tive characteristic, its sign must be changed to positive, 
after diminishing it by the unit, if any, carried in the sub- 
traction from the decimal part of the logarithm. Or, if 
the characteristic of the logarithm of the dividend is nega- 
tive, it must be treated as a negative number. 

EXAMPLES. 

1. To divide 24163 by 4567. 

log 24163 = 4.383151 
log 4567 = 3.659631 

Quotient, 5.29078 . . 0.723520 

2. To divide 0.06314 by .007241. 

log 0.06314 = 2.800305 
log 0.007241 = 3.859799 

Quotient, 8.7198 . . 0.940506 



Here, 1 carried from the decimal part to the 3, changes 
it to 2, which being taken from 2, leaves for the cha- 
racteristic. 

3. To divide 37.149 by :^;23.76. 

log 37.149 = 1.569947 
log 523.76 = 2.719133 

Quotient, 0.0709274 . 2.850814 



SEC. I] LOGARITHMS. 17 

4. To divide 0.7438 by 12.9476. 

log 0.7438 = 1.871456 
log 12.9476 = 1.112189 

Quotient, 0.057447 . . 2.759267 

Here, the 1 taken from 1, gives 2 for a result, as set 
down. 

ARITHMETICAL COMPLEMENT. 

13. Tlie Arithmetical complement of a logarithm is the 
number which remains after subtracting the logarithm 
from 10. 

Thus, 10 - 9.274687 = 0.725313. 

Hence, 0.725313 is the arithmetical complement 

of 9.274687. 

14. We will now show that, the difference hetween two 
logarithms is truly found^ hy adding to the first logarithm the 
arithmetical complement of the logarithm to he subtracted^ and 
then diminishing the sum hy 10. 

Let a = the first logarithm, 

Z> = the logarithm to be subtracted, 
and c= 10 —5 = the arithmetical complement of b. 

Now the difference between the two logarithms will be 
expressed by a — h. 

But, from the equation c = 10 — h, we have 
c-10=-h, 
hence, if we place for — h its value, we shall have 

a — h = a + c—10, 
which agrees with the enunciation. 

When we wish the arithmetical complement of a loga- 
rithm, we may write it directly from the table, by subtract- 
ing the left hand figure from 9, then proceeding to the right, 
subtract each figure from 9 till we reach the last significant 
figure," which must be taken from 10: this will he the same 
as taking the logarithm from 10. 
2 



18 ELEMEITTS OF SURVEYING. [BOOK I. 

EXAMPLES. 

1. From 3.274107 take 2.104729. 

By common method. By arith. comp. 

3.274107 3.274107 

2.104729 its ar. comp. 7.895271 

Diff. 1.169378 Sum 1.169378 after sub- 

tracting 10. 

Hence, to perform division by means of tbe aritbmetical 
complement, we bave tbe following 

RULE. 

To the logarithm of the dividend add the ariilimetical com- 
plement of the logarithm of the divisor: the sum^ after sub- 
tracting 10, will be the logarithm of the quotient. 

EXAMPLES. 

1. Divide 327.5 by 22.07. 

log 327.5 2.515211 

log 22.07 ar. comp. 8.656198 

Quotient, 14.839 . . . 1.171409 

2. Divide 0.7438 by 12.9476. 

log 0.7438 .... 1.871456 
log 12.9476 ar. comp. 8.887811 

Quotient, 0.057447 . . . 2.759267 

In tbis example, the sum of tbe characteristics is 8, 
from which, taking 10, the remainder is 2, 

3. Divide 37.149 by 523.76. 

log 37.149 .... 1.569947 
log 523.76 ar. comp. 7.280867 

Quotient, 0.0709273 . . 2.850814 



EC. 11] GEOMETRICAL DEFINITIONS. 1| 

4. Divide 0.875 by 25. Ans. 0.035. 

5. Divide 3.1416 by .944. Ans. 3.3279. 

6. Divide 2756 by 327. Ans. 8.4281. 

7. Divide 672859 by 0.09657. Ans. 6967580.64. 



SECTION II. 

GEOMETEICAL DEFINITIONS AND CONSTKUCTIONS. 

1. Extension has tbree dimensions, length, breadtb, 
and thickness. 

2. GrEOMETRY is the science which has for its object : 
1st. The measurement of extension ; and 2dly. To dis- 
cover, by means of such measurement, the properties and 
relations of geometrical figures. 

3. A Point is that which has place, or position, but 
not magnitude. 

4. A Line is length, without breadth or thickness. 

5. A Straight Line is one which 

lies in the same direction between any ■ 

two of its points. 

6. A Broken Line is one made up 
of straight lines, not lying in the same 
direction. 

7. A Curve Line is one which 
changes its direction at every point. 

The word line when used alone, will designate a straight 
line ; and the word curve, a curve line. 

8. A Surface is that which has length and breadth 
without thickness. 




20 



ELEMENTS OF SURVEYING. [BOOK I, 



9. A Plake is a surface, sucli, tliat if any two of its 
points be joined by a straight line, such line will be wholly 
in the surface. 

10. Every surface, which is not a plane surface, or com- 
posed of plane surfaces, is a curved surface. 

11. A Solid, or Body is that which has length, breadth, 
and thickness : it therefore combines the' three dimensions 
of extension. 

12. An Akgle is the portion of a plane included be- 
tween two straight lines which meet at a common point. 
The two straight lines are called the sides of the angle, 
and the common point of intersection, the vertex. 

Thus, the part of the plane includ- 
ed between AB and AC is called an 
angle : AB and A are its sides^ and A 
its vertex. 

An angle is sometimes designated 
simply by a letter placed at the vertex, 
as, the angle A ; but generally, by three letters, as, the 
angle BA G or OAB^ — the letter at the vertex being always 
placed in the middle. 

13. When a straight line meets an- 
other straight line, so as to make the 
adjacent angles equal to each other, 
each angle is called a right angle ; and 
the first line is said to be jperpendicu- 
lar to the second. 




14. An Acute Angle is an angle 
less than a right angle. 



15. An Obtuse Angle is an 
greater than a right angle. 



SEC. IT.] GEOMETRICAL DEFINITIONS. 21 

16. Two straiglit lines are said to 

be parallel, wlien being situated in 

tlie same plane, they cannot meet, how 
far soever, either way, both of them 
be produced. 

17. A Plane Figure is a portion of a plane terminat- 
ed on all sides by lines; either straight or curved. 

18. A Polygon, or rectilineal fig- 
ure, is a portion of a plane terminat- 
ed on all sides by straight lines. 

The sum of the bounding lines is 
called the jperimeter of the polygon. 

19. The polygon of three sides, the simplest of all, is 
called a triangle; that of four sides, a quadrilateral; that 
of five, a pentagon ; that of six, a hexagon ; that of seven, 
a heptagon ; that of eight, an octagon ; that of nine, an 
nonagon ; that of ten, a decagon ; and that of twelve, a 




20. An Equilateral polygon is one which has all its 
sides equal ; an equiangular polygon, is one which has aU 
its angles equal. 

21. Two polygons are mutually equilateral, when they 
have their sides equal each to each, and placed in the 
same order: that is to say, when following their bounding 
lines in the same direction, the first side of the one is 
equal to the first side of the other, the second to the 
second, the third to the third, and so on, 

22. Two polygons are mutually equiangular, when every 
angle of the one is equal to a corresponding angle of the 
other, each to each. 

23. Triangles are divided into classes with reference 
both to their sides and angles. 



1. An 
which has its three sides equal. 




22 



ELEMENTS OF SURVEYING. [BOOK I. 



2. An isosceles triangle is one wMcli 
tas only two of its sides equal. 




8. A scalene triangle is one "vvkicli lias 
its three sides unequal. 



4. An aciii&- 
wHcli lias its tliree 



acute. 



5. A right-angled triangle is one wMdi 
has a right angle. The side opposite the 
right angle is called the hypothenuse^ and 
the other two sides, the hase and perpen- 
dicular. 



6. An obtuse-angled triangle is one 
which has an obtuse angle. 



24. There are three kinds of Quadkilaterals ; 




1. The trapezium^ which has none of 
its sides parallel. 




2. The trapezoid^ which has only two 
of its sides parallel. 



8. The parallelogram^ which has its 
opposite sides parallel. 



SEC.II] GEOMETRICAL DEFINITIONS. 

25. There are four kinds of Parallelograms: 



23 



1, The rJiomboid, which has no right 
angle. 



dJ 



2. The rhombus , or lozenge, which is 
an ecLuilateral rhomboid. 



3, The rectangle, which is an equian- 
gular parallelogram, but not equilateral. 



4. The square, which is both equilat- 
eral and equiangular. 



A Diagonal of a figure is a line 
•\yhich joins the vertices of two angles 
not adjacent. 




EXPLANATION OF SIGNS. 

26. The sign = is the sign of equality; thus, the ex- 
pression A = B, signifies that A is equal to B. 

27. To signify that A is smaller than B, the expression 
A <C B is used. 

28. To signify that A is greater than B, the expression 
J. > jB is used ; the smaller quantity being always at the 
vertex of the angle. 

29. The sign + is called plus ; it indicates addition. 



24 ELEMENTS OF SURVEYING. [BOOK I. 

SO. The sign — is called minus ; it indicates subtraction : 
Thus, A+B, represents the sum of the quantities A 
and B; A — B represents their difference, or what remains 
after B is taken from A ; and A — B+ 0, or A + C — B^ 
signifies that A and are to be added together, and that 
B is to be subtracted from their sum. 



31. The sign X indicates multiplication : thus Ax B 
represents the product of A and B. 

The expression Ax {B-{- C— D) represents the product 
of J. by the quantity B+C—D. li A + D were to be 
multiplied by A — B-\- G, the product would be indicated 
thus; 

{A+D)x{A-B+Cl 

whatever is enclosed within the curved lines, being consid- 
ered as a single quantity. The same thing may also be 
indicated by a bar : thus, 



A + B+CxD, 

denotes that the sum of J., B and (7, is to be multiplied 
hj D. 

82. A figure placed before a line, or quantity, serves 
as a multiplier to that line or quantity; thus, ^AB signi- 
fies that the line AB is taken three times ; ^A signifies the 
half of the angle A. 

83. The square of the line AB is designated by AB~ ; 
its cube by AB . What is meant by the square and cube 
of a line is fully explained in Geometry. 

34, The sign -y/ indicates a root to be extracted; thus, 
■v/2 means the square-root of 2 ; -/ J. X B means the square- 
root of the product of A and B. 



SEC. II.] GEOMETRICAL CONSTRUCTIONS. 



25 



GEOMETRICAL CONSTRUCTIONS. 



35. Before explaining the method of constructing geo- 
metrical problems, we shall describe some of the simpler 
instruments and their uses. 



DIVIDERS. 




36. The dividers is the most simple and useful of the 
instruments used for drawing. It consists of two legs ha, 
he, which may be easily turned around a joint at h. 

One of the principal uses of this instrument is to lay 
off on a line, a distance equal to a given line. 

For example, to lay off on CD a distance equal to AB. 

For this purpose, place the forefin- 
ger on the joint of the dividers, and A\ B 

set one foot at A: then extend, with 

the thumb and other fingers, the ^' -^ — 2> 

other leg of the dividers, until its foot reaches the point 
B. Then raise the dividers, place one foot at (7, and 
mark with the other the distance GE : this will evidently 
be equal to AB. 



RULER AND TRIANGLE. 




37. A Euler of convenient size, is about twenty inches 
in length, two inches wide, and a fifth of an inch in thick- 



26 ELEMENTS OF SURVEYING. [BOOK I. 

ness. It should be made of a laard material, perfectly 
straight and smooth. 

The hypothenuse of the right-angled triangle, which is 
used in connection with it, should be about ten inches in 
length, and it is most convenient to have one of the sides 
considerably longer than the other. We can solve, with 
the ruler and triangle, the two following problems. 

I. To draw through a given point a line which shall be paral- 
lel to a given line. 

38. Let be the given point, and AB the given line. 

Place the hypothenuse of the tri- o 

angle against the edge of the ruler, 

and then place the ruler and triangle , , 

on the paper, so that one of the 

sides of the triangle shall coincide exactly with AB: the 

triangle being below the line. 

Then placing the thumb and fingers of the left hand 
firmly on the ruler, slide the triangle with the other hand 
along the ruler until the side which coincided with AB 
reaches the point G. Leaving the thumb of the left hand 
on the ruler, extend the fingers upon the triangle and hold 
it firmly, and with the right hand, mark with a pen or 
pencil, a line through C: this line will be parallel to AB. 



IL To draw through a given point a line which shall he per- 
pendicular to a given line. 

89. Let AB be the given line, and D the given point. 

Place the hypothenuse of the tri- 
angle against the edge of the ruler, as 

before. Then place the ruler and | 

triangle so that one of the sides of 
the triangle shall coincide exactly with the line AB. 
Then, slide the triangle along the ruler until the other 
side reaches the point I): draw through J) a right line, 
and it will be perpendicular to AB. 



SEC. II.] GEOMETRICAL CONSTRUCTIONS. 



27 



SCALE OF EQUAL PARTS. 



.1 .2 .n.U.B .6 .7 .8 .D7i 



40. A scale of equal parts is formed by dividing a line 
of a given length into equal portions. 

If, for example, the line a6 of a given length, say one 
inch, be divided into any number of equal parts, as 10, 
the scale thus formed, is called a scale of ten parts to the 
inch. The line a&, which is divided, is called the unit of 
the scale. This unit is laid off several times on the left 
of the divided line, and the points marked 1, 2, 8, &c. 

The unit of scales of equal parts, is, in general, either 
an inch, or an exact part of an inch. If, for example, ah, 
the unit of the scale, were half an inch, the scale would 
be one of 10 parts to half an inch, or of 20 parts to the 
inch. 

If it were required to take from the scale a line equal 
to two inches and six -tenths, place one foot of the dividers 
at 2 on the left, and extend the other to .6, which marks 
the sixth of the small divisions: the dividers will then 
embrace the required distance. 

DIAGONAL SCALE OF EQUAL PARTS. 







M / / / / 1 / 






oa 


1 / \ \ \ \ \ ] 






08 


\\ 1 /yi 1 1 1 1 






07 


\ \ \ \ \ \ M ' 






06 


MM'' '1 






05 


/ W i ' ' ' 






or 


/ 1 






03 


\ \ \ \ \ \ \ 






OZ 


\ \ I \\ \ \ 






01 


M / M , (i 



a.l .3.3.4.5.6.7. 



41. This scale is thus constructed. Take ah for the 
unit of the scale, which may be one inch, -|, |- or f of an 
inch, in length. On ah describe the square ahcd. Divide 
the sides ah and dc each into ten equal parts. Draw af 
and the other nine parallels as in the figure. 

Produce ha to the left, and lay off the unit of the 
scale any convenient number of times, and mark the points 



28 ELEMEN-TS OF SURVEYING. [BOOKI. 

1, 2, 3, &c. Then, divide the line ad into ten equal parts, 
and through the points of division draw parallels to ah, as 
in the figure. 

Now, the small divisions of the line ah are each one- 
tenth (.1) of ah ; they are therefore .1 of ad, or .1 of ag 
or gh. 

If we consider the triangle adf, we see that the base df 
is one-tenth of ad, the unit of the scale. Since the distance 
from a to the first horizontal line above ah, is one-tenth of 
the distance ad, it follows that the distance measured on that 
line between ad and af is one-tenth of df: but since one-tenth 
of a tenth is a hundredth, it follows that this distance is 
one hundredth (.01) of the unit of the scale. A like dis- 
tance measured on the second line will be two hundredths 
(.02) of the unit of the scale ; on the third, .03 ; on the 
fourth, .04, &c. 

If it were required to take, in the dividers, the unit of 
the scale, and any number of tenths, place one foot of the 
dividers at 1, and extend the other to that figure between 
a and h which designates the tenths. If two or more 
units are required, the dividers must be placed on a point 
of division further to the left. 

When units, tenths, and hundredths, are required, place 
one foot of the dividers where the vertical line through 
the point which designates the units, intersects the line 
which designates the hundredths : then, extend the dividers 
to that line between ad and he which designates the tenths : 
the distance so determined will be the one required. 

For example, to take off the distance 2.34, we place 
one foot of the dividers at I, and extend the other to e: 
and to take off the distance 2.58, we place one foot of the 
dividers at p and extend the other to q. 

Eemark I. If a line is so long that the whole of it 
cannot be taken from the scale, it must be divided, and 
the parts of it taken fi-om the scale in succession. 

Eemark II. If a line be given upon the paper, its 
length can be found by taking it in the dividers and ap- 
plying it to the scale. 



SEC. II.] GEOMETRICAL CONSTRUCTIONS. 



29 



SCALE OF CHORDS. 




42. If, "witli any radius, as AG^ we describe the quad- 
rant CZ), and then divide it into 90 equal parts, each part 
is called a degree. 

Through C, and each point of division, let a chord be 
drawn, and let the lengths of these chords be accurately 
laid off on a scale : such a scale is called a scale of chords. 
In the figure, the chords are drawn for every ten de- 
grees. 

The scale of chords being dnce constructed, the radius 
of the circle from which the chords were obtained, is 
known; for, the chord marked 60 is always equal to the 
radius of the circle. A scale of chords is generally laid 
down on the scales which belong to cases of mathematical 
instruments, and is marked cho. 



(l>.- 



To lay off, at a given point of a line, with the scale of chords, 
an angle equal to a given angle. 

43. Let AB be the line, and A the given point. 

Take from the scale the chord of 60 
degrees, and with this radius and the 
point ^ as a centre, describe the arc 

BC. Then take from the scale the 

chord of the given angle, say 30 de- "^ ^ 

grees, and with this line as a radius, and 5 as a centre, 
describe an arc cutting BG in G. Through A and G 
draw the hne AG, and BAG will be the required angle. 



30 ELEMENTS OF SURVEYING. [BOOK I. 



SEMICIRCULAR PROTRACTOR. 
C 




A 

44. This instrument is used to lay down, or protract 
angles. It may also be used to measure angles included 
between lines already drawn upon paper. 

It consists of a brass semicircle, ABO, divided to balf 
degrees. The degrees are numbered from to 180, both 
ways ; that is, from J. to ^ and from B to A. The di- 
visions, in the figure, are made only to degrees. There 
is a small notch at the middle of the diameter AB, which 
indicates the centre of the protractor. 

To lay off an a^igle with a Protractor. 

45. Place the diameter AB on the line, so that the 
centre shall fall on the angular point. Then count the 
degrees contained in the given angle from A towards B, or 
from B towards J., and mark the extremity of the arc with 
a pin. Eemove the protractor, and draw a line through 
the point so marked and the angular point : this line will 
make with the given line the required angle. 

SECTORAL SCALE OF EQUAL PARTS. 




SEC. II.] GEOMETRICAL CONSTRUCTIONS. 31 

46. The sector is an instrument generally made of ivory 
or brass. It consists of two arms, or sides, which, open 
by turning round a joint at their common extremity. 

There are several scales laid down on the sector : those, 
however, which are chiefly used in drawing lines and 
angles, are, the scale of chords already described, and the 
scale of equal parts now to be explained. 

On each arm of the sector, there is a diagonal line 
that passes through the point about which the arms turn : 
these diagonal lines are divided into equal parts. 

On the sectors which belong to the cases of English 
instruments, the diagonal lines are designated by the letter 
Jv, and numbered from the centre of the sector, 1, 2, 3, 4, 
5, 6, 7, 8, 9, 10, to the two extremities. On the sectors 
which belong to cases of French instruments, they are de- 
signated, " Les parties egales," and numbered 10, 20, 30, 
40, &c., to 200. On the English sectors there are 20 equal 
divisions between any two of the lines numbered 1, 2, 3, 
&c., so that there are 200 equal parts on the scale. 

The advantage of the sectoral scale of equal parts, is 
this — 

When it is proposed to draw a line upon paper, on 
such a scale that any number of parts of the line, 40 for 
example, shall be represented by one inch on the paper, or 
by any part of an inch, take the inch, or part of the inch, 
from the scale of inches on the sector : then, placing one 
foot of the dividers at 40 on one arm of the sector, open 
the sector until the other foot reaches to the corresponding 
number on the other arm : then lay the sector on the table 
without varying the angle. 

Now, if we regard the lines on the sector as the sides 
of a triangle, of which the line 40, measured across, is the 
base, it is plain, that if any other line be likewise meas- 
ured across the angle of the sector, the bases of the tri- 
angles, so formed, will be proportional to their sides. 
Therefore, if we extend the dividers from 50 to 50, this 
distance will represent a line of 50, to the given scale: 
and similarly for other lines. 



32 ELEMENTS OF SURVEYING-. [BOOK I. 

Let it now be required to laj down a line of sixtj- 
seven feet, to a scale of twenty feet to tlie incli. 

Take one inch from tlie scale of inches: then place 
one foot of the dividers at the twentieth division, and 
open the sector until the dividers will just reach the twen- 
tieth division on the other arm : the sector is then set to 
the proper angle ; after which the required distance to be 
laid down on the paper is found by extending the divi- 
ders from the sixty-seventh division on one arm, to the 
sixty-seventh division on the other. 

gutter's scale. 

47. This is a scale of two feet in length, on the faces 
of which a variety of scales is marked. The face on 
which the divisions of inches are made, contains, however, 
all the scales necessary for laying down lines and angles. 
These are, the scale of equal parts, the diagonal scale of 
equal parts, and the scale of chords, all of which have 
been described. 



SOLUTION OF PROBLEMS REQUIRING THE USE OF THE IN- 
STRUMENTS THAT HAVE BEEN DESCRIBED. 

I. At a given point in a given straight line, to erect a jperpen- 
dicular to the line. 

48. Let A be the given point, and BC the given line. 

From A lay off any two distances, \L^ 

AB and AC, equal to each other. 
Then, from the points B and C, as 
centres, with a radius greater than BA, 



describe two arcs intersecting each B A (J 

other in D : draw AD, and it will be the perpendicular 
required. " j 

11. From a given point without a straight line, to let fall a 
perpendicular on the line. 

49. Let A be the given point, and BD the given line. 



SEC.IL] GEOMETRICAL CONSTRUCTIONS. 



33 



From the point J. as a centre, 
with a radius sufficiently great, 
describe an arc cutting the line 
BD in the two points B and D: 
then mark a point E^ equally dis- 
tant from the points B and i), 
and draAV AE : AE will be the perpendicular required. 




III. At a jpoint, in a given line, to make an angle equal to a 
given angle. 

50. Let A be the given point, AE the given line, and 
IKL the given angle. 

From the vertex ^ as a 
centre, with any radius, describe 
the arc JX, terminating in the 
two sides of the angle. From 
the point J. as a centre, with a distance AE equal to KT, 
describe the arc ED; then take the chord LI, with which, 
from the point jE^ as a centre, describe an arc cutting the 
indefinite arc BE, in B; draw AB, and the angle EAB 
will be equal to the given angle K. 




IV. To divide a given angle, or a given arc^ into two equal 
parts. 

51. Let G be the given angle, and AEB the arc which 
measures it. * 

From the points A and B as 
centres, describe with the same 
radius two arcs cutting each other 
in B: through D and the centre 
G draw GB : the angle AGE will 
be equal to the angle EGB, and 
the arc AE to the arc EB. 




V. Through a given point to draio a parallel to a given line, 
52. Let A be the given point, and BG the given liiae. 



34 ELEMENTS OF SURVEYUiTG. [BOOK I 

From J. as a centre, with a /'' e^ 

radius greater than the shortest 
distance from A to BG^ describe 
the indefinite arc ED : from the ^'' 

point jG' as a centre, with the same radius, describe the 
arc AF ; make ED = AF, and draw AD: then will AD 
be the parallel required. 

YI. Two angles of a triangle heing given, to find the third. 

53. Draw the indefinite line 
DEF. At the point E, make 
the angle DEC equal to one of 
the given angles, and the angle 
GEH equal to the other : the re- 
maining angle HEF will be the 
third angle required. 



YII. To represent, on paper, a line of a given length, so that 
any number of its parts shall correspond to the unit of the 



54. Suppose that the given line were 75 feet in length, 
and it were required to draw it on paper, on a scale of 25 
feet to the inch. 

The length of the line 75 feet, being divided by 25, 
will give 3, the number of inches which will represent the 
line on paper. 

Therefore, draw the indefinite line AB, on which lay 



-i~£ 



off a distance A G equal to 3 inches : A G will represent 
the given line of 75 feet, drawn on the required scale. 

Ee^ark I. This problem explains the manner of repre- 
senting a line upon paper, so that a given number of its 
parts shall correspond to the unit of the scale, whether 
that unit be an inch or any part of an inch. 

When the length of the line to be laid down is given, 
and it has been determined how many parts of it are to 



SEC. II.] GEOMETRICAL CONSTRUCTIONS. 35 

be represented on tlie paper by a distance equal to the 
unit of the scale, we find the length which is to be taken 
from the scale by the following 



RULE. 

Divide the length of the line hy the numher of parts which 
is to he represented hy the unit of the scale: the quotient will 
show the nuinher of units which is to he taken from ihe scale, 

EXAMPLES. 

1. If a line of 640 feet is to be laid down on paper, on 
a scale of 40 feet to the inch ; what length must be taken 
from the scale ? 

40)640(16 inches. 

2. If a line of 357 feet is to be laid down on a scale 
of 68 feet to the unit of the scale, (which we will suppose 
half an inch), how many parts are to be taken ? 

i j 5.25 parts, or 
( 2.625 inches. 

3. A line of 384 feet is drawn on paper, on a scale of 
45 feet to the inch ; what is its length on the paper ? 

Ans. 8.53 inches. 

Eemark II. When the length of a line on the paper is 
given, and it is required to find the true length of the 
line which it represents, take the line in the dividers and 
apply it to the scale, and note the number of units, and 
parts of a unit to which it is equal. Then multiply this 
number by the number of parts which the unit of the 
scale represents, and the product will be the length of the 
line. 

For example, suppose the length of a line drawn on 
the paper was found to be 3.55 inches, the scale being 40 
feet to the inch : then, 

3.55 X 40 = 142 feet, the length of the line. 



36 



ELEMENTS OF SURVEYING. "[BOOK I. 



VIII. Having given two sides and the included angle of a tri- 
angle, to describe the triangle. 

55. Let the line ^=150 feet, and = 120 feet, be tlie 
given sides ; and J. = 80 degrees, the given angle : to de- 
scribe the triangle on a scale of 200 feet to the inch. 

Draw the indefinite line i)(r, and 
at the point D, make the angle ODH 
equal to 30 degrees : then lay off 
DG equal to 150, equal to three 
quarters of an inch, and DH equal 
to 120, equal to six tenths of an 
inch, and draw GH: DHG will be the required triangle. 




IX. The three sides of a triangle being given, to describe the 
triangle. 

56. Let A, B and C, be the sides. 

Draw DE equal to the side A. 
From the point D as, 2, centre, with 
a radius equal to the second side B, 
describe an arc : from ^ as a cen- 
tre, with a radius equal to the third 
side (7, describe another arc inter- 
secting the former in F; draw DF and EF, and DFE will 
be the triangle required. 







X. Having given two sides of a triangle and an angle oppo- 
site one of them, to describe the triangle. 

57. Let A and B be the given sides, and the given 
angle, which we will suppose is opposite the side B. 

Draw the indefinite line DF 
and make the angle FDH equal to 
the angle C: take DH= A, from 
the point i?j as a centre, with a 
radius equal to the other given 
side, B, describe an arc cutting 
DF in F; draw HF: then will DHF be the required tri- 




SEC. II.] GEOMETRICAL CONSTRUCTIONS. 



37 



If the angle G is acute, and 
tlie side B less tlian J., then 
the arc described from the 
centre E with the radius EF 
= B will cut the side DF in 
two points, F and 6^, lying on 
the same side of D: hence, there will be two triangles, 
DEF, and DEG, either of which will satisfy all the condi- 
tions of the problem. 




XL The adjacent sicks of a parallelogram^ with the angle 
which they contain, being given, to describe the parol- 
lelogram. 

68. Let A and B be the given sides, and the given 
angle. 

Draw the line JDH, and jr/_ :^.jC; 

lay off BE equal to J. ; at / / ' 

the point B, make the angle ^Z /^ j£ 

EBF=0; take BF=B: de- A\ — i / 

scribe two arcs, the one from ^' ' 

F^ as a centre, with a radius FO = BE, the other from E, as 
a centre, with a radius EG = BF ; through the point G, 
where these arcs intersect each other, draw EG, EG ; BEGF 
will be the parallelogram required. 



XII. To find the centre of a given circle or arc. 

59. Take three points, A, B, 0, any where in the cir- 
cumference, or in the arc: 
draw AB, BG; bisect these two 
lines by the perpendiculars, BE, 
EG: the point 0, where these 
perpendiculars meet, will be the 
centre sought. 

The same construction serves 
for making a circumference pass 
through three given points A, B, ' -^ 

(7, and also for describing a circumference, about a given 
triangle. 




38 ELEMENTS OF SURVEYING. [BOOK I. 

PLANE TEIGONOMETRY. 



SECTION III. 



DEFINITIONS. — APPLICATION TO HEIGHTS AND DISTANCES. 

1. In every plane triangle tliere are six parts : three 
sides and three angles. These parts are so related to each 
other, that when one side and any two other parts are 
given, the remaining ones can be obtained, either by geo- 
metrical construction or by trigonometrical computation. 

2. Plane Trigonometry explains the methods of com- 
puting the unknown parts of a plane triangle, when a suf- 
ficient number of the six parts is given. 

3. For the purpose of trigonometrical calculation, the 
circumference of the circle is supposed to be divided into 
360 equal parts, called degrees ; each degree is supposed 
to be divided into 60 equal parts, called minutes; and 
each minute into 60 equal parts, called seconds. 

Degrees, minutes, and seconds, are designated respec- 
tively, by the characters ° ' ". For example, ten degrees, 
eighteen mimites^ and fourteen seconds^ would be written 
10° 18' 14". 

4. If two lines be drawn through the centre of the 
circle, at right angles to each other, they will divide the 
circumference into four equal parts, of 90° each. Every 
right angle then, as EOA, is measured by an arc of 90° ; 
every acute angle, as BOA^ by an arc less than 90° ; and 
every obtuse angle, as FOA^ by an arc greater than 90°. 

5. The complement of an arc is 
what remains after subtracting the 
arc from 90°. Thus, the arc UB 
is the complement of AB. The 
sum of an arc and its complement 
is equal to 90°. 

6. The supplement of an arc is 
what remains after subtracting the 
arc from 180°. 




SEC. I.] ' PLANE TRIGONOMETRY. 39 

supplement of the arc AEF. The sum of an arc and its 
supplement is equal to 180°. 

7. The sine of an arc is the perpendicular let fall from 
one extremity of the arc on the diameter which passes 
through the other extremity. Thus, BD is the sine of the 
arc AB. 

8. The cosine of an arc is the part of the diameter in- 
tercepted between the foot of the sine and centre. Thus, 
OD is the cosine of the arc AB. 

9. The tangent of an arc is the line which touches it at 
one extremity, and is limited by a line drawn through the 
other extremity and the centre of the circle. Thus, AG is 
the tangent of the arc AB. 

10. The secant of an arc is the line drawn from the 
centre of the circle through one extremity of the arc, and 
limited by the tangent passing through the other extremi- 
ty. Thus, 00 is, the secant of the arc AB. 

11. The four lines, BD, OD, AC, 00, depend for their 
values on the arc AB and the radius OA ; they are thus 
designated : 

sin AB for BD 

cos AB for OD 

tan AB for AQ 

sec AB for OC 

12. If ABE be equal to a quadrant, or 90°, then EB 
will be the complement of AB. Let the lines ET and IB 
be drawn perpendicular to OE. Then, 

ET, the tangent of EB, is called the cotangent of AB ; 
IB, the sine of EB, is equal to the cosine of AB ; 
OT, the secant of EB, is called the cosecant of AB. 

In general, if A is any arc or angle, we have, 
cos J. = sin (90°-^) 
cot A = tan (90° - A) 
cosec A = sec (90° — A) 



40 



ELEMEN-TS OF SURVEYIN-G. 



[BOOK 



13. If we take an arc, ABEF, 
greater than 90°, its sine will be 
FH ; OH will be its cosine ; A Q 
its tangent, and OQ its secant. 
But FH is tlie sine of tlie arc OF, 
wbicli is tbe supplement of AF, 
and OH is its cosine ; bence, the 
sine of an arc is equal to the sine of 
its supplement ; and the cosine of an 
arc is equal to the cosine of its supplement* 

Furtbermore, AQ is tbe tangent of tbe arc AF, and 
0^ is its secant: GL is tbe tangent, and OL tbe secant 
of tbe supplemental arc GF. But since ^^ is equal to 
GL, and OQ to OL, it follows tbat, the tangent of an arc 
is equal to the tangent of its supplement; and the secant of an 
arc is equal to the secant of its supplement.* 




TABLE OF NATUEAL SINES. 

14. Let US suppose, tbat in a circle of a given radius, 
tbe lengths of the sine, cosine, tangent, and cotangent, have 
been calculated for every minute or second of the quad- 
rant, and arranged in a table; such a table is called a 
table of sines and tangents. If tbe radius of tbe circle is 
1, tbe table is called a table of natural sines. A table of 
natural sines, therefore, shows the values of the sines, co- 
sines, tangents, and cotangents of all the arcs of a quad- 
rant, which is divided to minutes or seconds. 

If the sines, cosines, tangents, and secants are known 
for arcs less than 90°, those for arcs which are greater can 
be found from them. For if an arc is less than 90°, its 
supplement will be greater than 90°, and the numerical 
values of these lines are the same for an arc and its sup- 
plement. Thus, if we know tbe sine of 20°, we also know 
the sine of its supplement 160° ; for tbe two are equal to 
each other. The Table of Natural Sines, beginning at page 
63, of the tables shows the values of the sines and cosines 
only. 



* These relations are between the rmmerical values of the trigonometrical lines ; 
the algebraic signs, which they have in the different quadrants, are not considered. 



SEC. Ill] PLANE TRIGONOMETRY. 41 

TABLE OF LOGARITHMIC SINES. 

15. In this table are arranged the logarithms of the 
numerical values of the sines, cosines, tangents, and co- 
tangents of all the arcs of a quadrant, calculated to a ra- 
dius of 10,000,000,000. The logarithm of this radius is 10. 
In the first and last horizontal lines of each page, are writ- 
ten the degrees whose sines, cosines, &c., are expressed on 
the page. The vertical columns on the left and right, are 
columns of minutes. 

CASE I. 

To find, in the table, the logarithmic sine, cosine, tangent, or 
cotangent of any given arc or angle. 

16. If the angle is less than 45°, look for the degrees 
in the first horizontal line of the different pages : when the 
degrees are found, descend along the column of minutes, on 
the left of the page, till you reach the number showing the 
minutes : then pass along a horizontal line till you come into 
the column designated, sine, cosine, tangent, or cotangent, as 
the case may be : the number so indicated is the logarithm 
sought. Thus, on page 87, for 19° 55', we find, 

sine 19° 55' ... . 9.532312 

cos 19° 55' ... . 9.973215 

tan 19° 55' .... 9.559097 

cot 19° 55' ... . 10.440903 

17. If the angle is greater than 45°, search for the de- 
grees along the bottom line of the different pages : when the 
number is found, ascend along the column of minutes on the 
right hand side of the page, till you reach the number express- 
ing the minutes: then pass along a horizontal line into the 
column designated tang, cot, sine, or cosine, as the case may 
be : the number so pointed out is the logarithm required. 

18. The column designated sine, at the top of the page, 
is designated by cosine at the bottom ; the one designated 
tang, by cotang, and the one designated cotang, by tang. 

The angle found by taking the degrees at the top of 
the page, and the minutes from the left hand vertical column, 
is the complement of the angle found by taking the degrees 



42 ELEMENTS OF SURVEYING. [BOOK I. 

at tlie bottom of tlie page, and tlie minutes from the riglit 
hand column on the same horizontal line with the first. 
Therefore, sine, at the top of the page, should correspond 
with cosine, at the bottom ; cosine with sine, tang with 
cotang, and cotang with tang, as in the tables (Art. 12). 

If the angle is greater than 90°, we have only to sub- 
tract it from 180°, and take the sine, cosine, tangent, or 
cotangent of the remainder. 

The column of the table next to the column of sines, 
and on the right of it, is designated by the letter D. 
This column is calculated in the following manner. 

Opening the table at any page, as 42, the sine of 24° 
is found to be 9.609313 ; that of 24° 01', 9.609597 : their 
difference is 284 ; this being divided by 60, the number 
of seconds in a minute, gives 4.73, which is entered in the 
column D. 

Now, supposing the increase of the logarithmic sine to 
be proportional to the increase of the arc, and it is nearly 
so for 60", it follows, that 4.73 is the increase of the sine 
for 1". Similarly, if the arc were 24° 20', the increase of 
the sine for 1", would be 4.65. 

The same remarks are applicable in respect of the 
column D, after the column cosine, and of the column D, 
between the tangents and cotangents. The column i), be- 
tween the columns tangents and cotangents, answers to 
both of these columns. 

Now, if it were required to find the logarithmic sine 
of an arc expressed in degrees, minutes, and seconds, we 
have only to find the degrees and minutes as before ; then, 
multiply the corresponding tabular difference by the sec- 
onds, and add the product to the number first found, for 
the sine of the given arc. 

Thus, if we wish the sine of 40° 26' 28". 

The sine 40° 26' ... . 9.811952 
Tabular difference 2.47 , 
Number of seconds 28 . 



Product, 69.16 to be added 69.16 

Gives for the sine of 40° 26' 28". 9.812021. 



SEC. III.] PLANE TRIGONOMETRY. 43 

The decimal figures at the right are generally omitted 
in the last result ; but when they exceed five-tenths, the 
figure on the left of the decimal point is increased by 1 ; 
the logarithm obtained is then exact, to within less than 
one unit of its right hand place. 

The tangent of an arc, in which there are seconds, is 
found in a manner entirely similar. In regard to the co- 
sine and cotangent, it must be remembered, that they in- 
crease while the arcs decrease, and decrease as the arcs are 
increased ; consequently, the proportional numbers found 
for' the seconds, must be subtracted, not added. 

EXAMPLES. 

1. To find the cosine of 3° 40' 40". 

The cosine of 3° 40' . . . 9.999110 

Tabular difference .13 . 

Number of seconds 40 

Product, 5.20 to be subtracted 5.20 



Gives for the cosine of 3° 40' 40" 9.999105. 

2. Find the tangent of 37° 28' 31". 

Ans. 9.884592. 

3. Find the cotangent of 87° 57' 59". 

Ans. 8.550356. 



CASE II. 

To find the degrees, minutes^ and seconds answering to any 
given logarithmic sine, cosine, tangent, or cotangent. 

19. Search in the table, in the proper column, and 
if the number is found, the degrees will be shown either 
at the top or bottom of the page, and the minutes in the 
side column either at the left or right. 

But, if the number cannot be found in the table, take 
from the table the degrees and minutes answering to the 
nearest less logarithm, the logarithm itself, and also the 
corresponding tabular difference. Subtract the logarithm 
taken from the table from the given logarithm, annex two 



44 ELEMEISTTS OF SURVEYI]!^G, [BOOK I. 

ciphers to tlie remainder, and tlien divide tlie remainder 
by tlie tabular difference : the quotient will be seconds, 
and is to be connected with the degrees and minutes be- 
fore found : to be added for the sine and tangent, and 
subtracted for the cosine and cotangent, 

EXAMPLES. 

1. Find the arc answering to the sine 9.880054 
Sine 49° 20', next less in the table 9.879963 



Tabular difference, 1.81)91.00(60". 

Hence, the arc 49° 20' 50" corresponds to the given sine 
9.880054. 

2. Find the arc whose cotangent is 10.008688 
cot 44° 26', next less in the table 10.008591 



Tabular difference, 4.21)97.00(23". 

Hence, 44° 26' - 23" = 44° 25' 37" is the arc answering 
to the given cotangent 10.008688. 

3. Find the arc answering to tangent 9.979110. 

Am. 43° 37' 21". 

4. Find the arc answering to cosine 9.944599. 

Ans. 28° 19' 45". 

20. We shall now demonstrate the principal theorems 
of Plane Trigonometry. 

THEOEEM I. 

The sides of a plane triangle are proportional to the sines of 
their opposite angles. 

21. Let ABC be a triangle ; then will 

OB : OA :: sin A : sin B. 

For, with J. as a centre, and AD 
equal to the less side BO, as a ra- 
dius, describe the arc BI: and with 
^ as a centre and the equal radius -^ /?/// 
BO, describe the arc OL, and draw BE and OF perpen- 
dicular to AB: now BE is the sine of the angle A, and 




SEC. Ill] PLANE TRIGONOMETRY. 45 

OF is the sine of B^ to the same radius AB or BC. But 
by similar triangles, 

AB '. BE :\ AG '. CF. 

But AB being equal to BG^ we have 

BG : sin J. : : AG : sin J5, or 
BG : AG :: sin A : sin B. 

By comparing the sides AB, AG, in a similar manner, 
we should find, 

AB : AG : : sin G : sin B. 



THEOEEM II. 

In any triangle, the sum of the two sides containing either 
angle, is to their difference, as the tangent of half the sum of 
the two other angles, to the tangent of half their difference. 

22. Let A GB be a triangle : then will 
AB+AG : AB-AG : : tan ^{G+B) : tan \{G-B). 

With JL as a centre, and a A' 
radius AG, the less of the two 
given sides, let the semicircumfe- 
rence IFGE be described, meeting 
AB in I, and BA produced, in E. 

Then, 5^ will be the sum of the C"-- --'FGH 

sides, and BI their difference. Draw GI and AF. 

Since GAE is an outward angle of the triangle AGB, 
it is equal to the sum of the inward angles G and B (Bk. 
I., Prop. XXY., Cor 6). But the angle GIE being at the 
circumference, is half the angle GAE at the centre (Bk. III., 
Prop. Xyill.) ; that is, half the sum of the angles G and 
B, or equal to \{G-\-B). 

The angle AFG=AGB, is also equal to ABG+BAF; 
therefore, BAF= AGB- ABG. 

But, IGF=l{BAF) = ^^{AGB-ABG), or ^{G-B). 

With / and G as centres, and the common radius IG, 
let the arcs GB and IG be described, and draw the lines 
GE and IE perpendicular to IG. The perpendicular GE 
will pass through E, the extremity of the diameter lE^ 




46 



ELEMENTS OF SUR VE YI^-G. 



[BOOK I. 




since the right angle IGE must be 
inscribed in a semicircle. 

But GE is the tangent of CIE 
= 1{G+B)', and IH is the tan- 
gent of IGB^\{G-B\ to the 
common radius CI. 

But since the lines GE and IH are parallel, the tri- 
angles BHI and BGE are similar, and give the proportion, 

BE : BI :: GE : IH, or 

by placing for BE and BI, GE and IH, their values, we 
have 
AB + AG : AB-AG :: tan }{G+B) : tan i((7-^). 



GD-DB. 



THEOEEM III. 

In any plane triangle, if a line is draion from the vertical 
angle perpendicular to the base, dividing it into two segments : 
then., the whole base, or sum of the segments, is to the sum of 
the two other sides, as the difference of those sides to the differ- 
ence of the segments. 

23. Let BA C be a triangle, and AD perpendicular to the 
base ; then will 

BG : GA + AB :: GA-AB 

For, AB" = BD~ + AD^' 

(Bk. IV., Prop. XL); 

and A0'' = D0' + AD'' 

by subtraction, AG~ — AB" = 

gd'-bb^. 

But since the difference of -?> J> C 

the squares of two lines is equivalent to the rectangle con- 
tained by their sum and difference (Bk. lY., Prop. X.), we 
have, 

AG^ - AB" = {A G+ AB) . {A G- AB) 

and GD^-DB~^{GD^DB). {GD-DB) 

therefore, {GD + DB).{GD-DB) = {AG +AB). {AG -AB) 
hence, GD + DB : AG+AB :: AG-AB : GD-DB. 




SEC. III.] PLANE TRIGONOMETRY. 47 



THEOREM IV. 

In any right-angled plane triangle^ radius is to the tangent 
of either of tlie acute angles, as the side adjacent to the side 
opposite. 

24. Let GAB be tlie proposed triangle, and denote the 
radius by R : then will ^ 

R : ioxi G :: AC : AB. ^^^ 

For, witb any radius as CD de- 



scribe the arc DH, and draw the tan- -^ 

gent DG. 

From, the similar triangles GDG and GAB, we have, 

OD : DG :: GA : AB; hence, 
R : tsin G :: GA : AB. 

By describing an arc with ^ as a centre, we could 
show in the same manner that, 

R : tan 5 : : AB : AC. 



THEOREM V. 

In every right-angled plane triangle, radiics is to the cosine 
of either of the acute angles, as the hypothenuse to the side 
adjacent. 

25. Let ABC be a triangle, right-angled at B: then will, 

R : cos J. : : AG : AB. c 

For, from the point J. as a centre, 
with any radius as AD, describe the 
arc DF, which will measure the angle '^^ ~EF^ 
A, and draw DE perpendicular to AB: then will AE be 
the cosine of A. 

The triangles ADE and AGB, being similar, we have, 

AD : AE :: AG : AB: that is, 
R : cos J. : : AG : AB. 

Remark. The relations between the sides and angles 
of plane triangles, demonstrated in these five theorems, are 




48 ELEMENTS OF SURVEYING. [BOOK I 

sufficient to solve all the cases of Plane Trigonometry. 
Of the six parts which make up a plane triangle, three 
must be given, and at least one of these a side, before the 
others can be determined. 

If the three angles only are given, it is plain, that an 
indefinite number of similar triangles may be constructed, 
the angles of which shall be respectively equal to the 
angles that are given, and therefore, the sides could not be 
determined. 

Assuming, with this restriction, any three parts of a 
triangle as given, one of the four following cases will al- 
ways be presented, 

I. When two angles and a side are given. 
II. "When two sides and an opposite angle are given. 
III. When two sides and the included angle are given. 
ly. When the three sides are given. 

CASE I. 
When two angles and a side are given. 

26. Add the given angles together, and subtract their 
sum from 180 degrees. The remaining parts of the tri- 
angle can then be found by Theorem I. 

EXAMPLES. 

1. In a plane triangle, ABG, 
there are given the angle J. = 58° 07', 
the angle B=2T 87', and the side 
J.5= 408 yards. Eequired the oth- 
er parts. 

GEOMETKICALLY. 

27. Draw an indefinite straight line, AB, and from the 
scale of equal parts lay off AB equal to 408. Then, 
at J., lay off an angle equal to 58° 07', and at B an angle 
equal to 22° 87', and draw the lines AG and BG : then 
will ABG be the triangle required. 

The angle G may be measured either with the protractor 
or the scale of chords (Sec. II., Arts. 42 and 44), and will be 




SEC. III.] PLANE TRIGONOMETRY. 49 

found equal to 99° 16'. The sides AG and BO may be 
measured by referring tbem to the scale of equal parts 
(Sec. II., Art. 40). We shall find ^ C= 158.9 and £C-= 351 
yards. 

TRIGOKOMETRICALLY BY LOGARITHMS. 

To the angle . . . A = 5S° 07' 
Add the angle . . J5=22°87' 

Their sum, = 80° 44' 

taken from . . . 180° 00' 



leaves . . . . 99° 16', of which, as it ex- 

ceeds 90°, we use the supplement 80° 44'. 

To find the side BO. 

As sin 99° 16' ar. comp. 0.005705 

: sin ^ 58° 07' 9.928972 

: : AB 408 2.610660 



: BO 351.024 (after rejecting 10) 2.545337. 

Eemark. The logarithm of the fourth term of a pro- 
portion is obtained by adding the logarithm of the second 
term to that of the third, and subtracting from their sum 
the logarithm of the first term. But to subtract the first 
term is the same as to add its arithmetical complement 
and reject 10 from the sum (Sec. I., Art. 13) : hence, the arith- 
metical complement of the first term added to the loga- 
rithms of the second and third terms, minus ten, will give 
the logarithm of the fourth term. 

To find the side A 0. 

As sin C 99° 16' ar. comp. 0.005705 

sin B 22° 37' 9.584968 

AB 408 2.610660 



AO 158.976 2.201333 



2. In a triangle ABO^ there are given A = 38° 25', 
^ = 57° 42', and AB = 'iOO: required the remaining parts. 
Ans. C=83°53', ^(7=249.974, ^C= 340.04. 
4 



50 



ELEMENTS OF SURVEYING. [BOOK I. 



CASE II. 
When two sides and an opposite 

28. In a plane triangle, ABC, 
there are given AC= 216, (75= 117, 
the angle A = 22° 37', to find the 
other parts. 



are given. 




GEOMETRICALLY. 

29. Draw an indefinite right line ABB' : from any 
point, as A, draw AC, making BAC= 22° 37', and make 
AC =216. With C as a centre, and a radius equal to 117, 
the other given side, describe the arc B'B; draw B'C and 
BC: then will either of the triangles ABC or AB'C, an- 
swer all the conditions of the question. 



TRIGONOMETRICALLY. 
To find the angle B. 

As BC 117 ar. comp. 7.931814 

AC 216 2.334454 

sin ^ 22° 37' 9.584968 

sin B' 45° 13' 55", or ABC 134° 46' 05" 9.851236. 



The ambiguity in this, and similar examples, arises in 
consequence of the first proportion being true for either 
of the angles ABC, or AB'C, which are supplements of 
each other, and therefore, have the same sine (Art. 13). 
As long as the two triangles exist, the ambiguity will con- 
tinue. But if the side CB, opposite the given angle, is 
greater than AC, the arc BB' will cut the line ABB', on 
the same side of the point A, in but one point, and then 
there will be only one triangle answering the conditions. 

If the side CB is equal to the perpendicular Cd, the 
arc BB' will be tangent to ABB', and in this case also 
there will be but one triangle. When CB is less than the 
perpendicular Cd, the arc BB' will not intersect the base 
ABB', and in that case, no triangle can be formed, or it 
will be impossible to fulfil the conditions of the problem. 




SEC. Ill] Pl^ANE TRIGONOMETRY. 51 

2, Given two sides of a triangle 50 and 40 respectively, 
and the angle opposite the latter equal to 32° : required 
the remaining parts of the triangle. 

Am. If the angle opposite the side 50 is acute, it is 
equal to 41° 28' 59" ; the third angle is then equal to 
106° 81' 01", and the third side to 72.368. If the angle 
opposite the side 50 is obtuse, it is equal to 138° 31' 01", 
the third angle to 9° 28' 69", and the remaining side to 
12.436. 

CASE III. 
When the two sides and their included angle are given. 

30. Let ABC be a triangle ; AB, 
BG, the given sides, and B the 
given angle. 

Since B is known, we can find 
the sum of the two other angles : 
for 

A+G^1%0°-B, and, 
^{A + C) = l{l^Q°-B). 

We next find half the difference of the angles A and 
G by Theorem II., viz., 

BG+BA : BG-BA :: tan ^(A+G) : tani(^-C), 

in which we consider BG greater than BA, and therefore 
A is greater than (7; since the greater angle must be op- 
posite the greater side. 

Having found half the difference of A and G, by add- 
ing it to the half sum, |( A + G\ we obtain the greater 
angle, and by subtracting it from half the sum, we obtain 
the less. That is, 

^{A -f C) + ^{A -C) = A, and 
-l{A+G)-i{A-G)=G 

Having found the angles A and G, the third side AG 
may be found by the proportion, 

sin Jl : sin jB : : BG : AG. 



52 ELEMENTS OF SURVEYING. [BOOK L 

EXAMPLES. 

1. In the triangle ABC, let BG=54,0, AB = ^50, and 
the included angle B = 80° : required the remaining parts. 

GEOMETRICALLY. 

81. Draw an indefinite right line BO, and from any 
point, as B, lay off a distance BG=b4S). At B make the 
angle CBA = 80° : draw BA, and make the distance 
BA = 4:50; draw AC; then will ABC he the required tri- 
angle. 

TRIGONOMETRICALLY. 

B0+ BA = 540 + 450 = 990 ; and BC-BA = 540 - 450 = 90. 
A+C= 180° -B= 180° - 80° = 100°, and therefore, 
i(^+(7)-i(100°) = 50°. 

To find ^{A - C). 

As BC+BA 990 ar. comp. 7.004365 

: BC-BA 90 1.954243 

t: tani(^+C) 50° 10.076187 

: tan ^{A - C) 6° 11' 9.034795. 

Hence, 50° + 6° 11' = 56° 11' = ^!; and 50° -6° 11' = 
43° 49' = a 

To find the third side A C. 

As sin C 43° 49' ar comp. 0.159672 

sin ^ 80° 9.998351 

AB 450 2.653213 



AC 640.082 . 2.806236. 



2. Given two sides of a plane triangle, 1686 and 960, 
and their included angle 128° 04' : required the other parts. 
Ans. Angles, 33° 34' 39" ; 18° 21' 21" ; side 2400. 



CASE IV. 



82. Having given the three sides of a plane triangle, 
to find the angles. 



SEC. Ill] PLANE TRIGONOMETRY. 



53 



Let fell a perpendicular from the angle opposite tlie 
greater side, dividing the given triangle into two right- 
angled triangles : then find the difference of the segments 
of the base by Theorem III. Half this difference being 
added to half the base, gives the greater segment ; and, 
being subtracted from half the base, gives the less segment 
Then, since the greater segment belongs to the right-angled 
triangle having the greater hypothenuse, we have two 
sides and the right angle of each of two right-angled tri- 
angles, to find the acute angles. 

EXAMPLES. 



1. The sides of a plane triangle 
being given ; viz., BG= 40, AG= 34, 
and AB = 25 : required the angles. 




GEOMETRICALLY. 



33. With the three given lines as sides construct a tri- 
angle as in Prob. IX. Then measure the angles of the 
triangle either with the protractor or scale of chords. 



As BG 
That is, 

Then, 

And, 



TRIGONOMETRICALLY. 

AG-\-AB :: AG-AB 



40 : 59 

40 + 13.275 

2 
4Q- 13.275 



o 59x9 

= 26.6375= GD, 
= 13.3625 = BB. 



GB-BB, 
= 13.275. 



In the triangle BAG, to find the angle BAG. 

As AG 34 ar. comp. 8.468521 

BG 26.6375 1.425493 

sin J9 90° 10.000000 

sin BAG 5r«84'40" 9.894014. 



54 



ELEMENTS OF SURVEYING. 



[BOOK I. 



In the triangle BAD, to find the angle BAD. 

AB 25 ar. comp. 8.602060 

BD 13.3625 1.125887 

sin Z> 90° 10.000000 

sin BAD 32° 18' 35" .... 



9.727947. 



Hence, 90° - DAG-^ 90° - 51° 34' 40" = 38° 25' 20" = C, 
and, 90°-5.4Z>=90°-32°18'35" = 57°41'25" = ^, 
and, BAD + DAG= 51° 34' 40" + 32° 18' 35" = 83° 53' 
15" = A. 

2. In a triangle, of wiiicli the sides are 4, 5, and 6, 
what are the angles ? 

Ans. 41° 24' 35"; 55° 46' 16"; and 82° 49' 09". 



SOLUTION OF EIGHT-ANGLED TEIANGLES. 

34. The unknown parts of a right-angled triangle may- 
be found by either of the four last cases ; or, if two of the 
sides are given, by means of the property that the square 
of the hypothenuse is equivalent to the sum of the squares 
of the two other sides. Or the parts may be found by 
Theorems IV. and V. 

EXAMPLES. 

1. In a right-angled triangle 
BAG, there are given the hypothe- 
nuse ^(7=250, and the base AG= 
240: required the other parts. 



As 



BG 

AG 
sin A 

sin B 



To find the angle B. 

250 ar. comp. 7.602060 

240 2.380211 

90° . . , 10.000000 



73° 44' 23" 9.982271. 



But C= 90° - ^ = 90° - 73° 44'^3" = 16° 15' 37" : 



S ^C. Ill] PLANE TRIGONOMETRY. 65 

Or C may he found from the proportion. 
As CB 350 ar. comp. 7.602060 

AC 240 2.380211 

R 10.000000 



cos G 16° 15' 37" 9,982271. 



To find side AB hy Theorem IV. 

As E ar. comp. 0.000000 

: tan G 16° 15' 37" 9.464889 

: : AG 240 2.380211 



AB 70.0003 1.845100. 



2. In a riglit-angled triangle BAG, there are given 
AG =384:, and ^=53° 08': required the remaining parts. 
Ans. AB= 287.96; BG = 4:79.979 ; (7= 36° 52'. 

. APPLICATION TO HEIGHTS AND DISTANCES. 

L To determine the horizontal distance to a point which is in- 
accessible hy reason of an intervening river.* 

35. Let G be the point. Measure 
along the bank of the river a hori- 
zontal base line AB, and select the -^^ 

stations A and B, in such a man- 
ner that each can be seen from the 
other, and the point G from both 
of them. Then measure the hori- . 

zontal angles GAB and GBA, with 
an instrument adapted to that purpose. 

Let us suppose that we have found AB = 600 yards, 
CA^ = 57°35', and GBA = 64:° 5V. 

The angle G= 180° -{A + B) = 57° 34'. 

To find the distance BG. 

As sin G 57° 34' ar. comp. 0.073649 

: sin J. 57° 35' 9.926431 

:i AB 600 2.778151 

: BG 600.11 yards 2.778231. 

* Read, definitions, from 3 to 14. roaffes 64- and fiR. 




56 ELEMENTS OF SURVEYING. [BOOK L 

To find the distance A G. 

As sin 57° 34' ar. comp. 0.078649 

: sin 5 64° 51' 9.956744 

:: AB 600 2.778151 

: ■ AC 643.94 yards 2.808544. 



II. To determine the altitude of an inaccessible object above a 
given horizontal plane. 

FIRST METHOD. 

36. Suppose D to be tlie inac- d 

cessible object, and BO the bori- ^^"'"'''"^S^. 

zontal plane from which the alti- „ =--r:.C^^ =:=-^/f^J^r 

tude is to be estimated : then, if \/' / /' \ ir, 

we suppose DG io be a vertical \ /y'>''' 

line, it will represent the required \ "<;'''' ' 

distance. ^ 

Measure any horizontal base line, as BA ; and at the 
extremities B and J., measure the horizontal angles GBA 
and GAB. Measure also the angle of elevation DBG. 

Then in the triangle GBA there will be known, two 
angles and the side AB\ the side BO can therefore be 
determined. Having found BO^ we shall have, in the 
right-angled triangle DBG^ the base BO and the angle at 
the base, to find the perpendicular DG, which measures 
the altitude of the point D above the horizontal plane BO. 

Let us suppose that we have found 

BA = 780 yards, the horizontal angle GBA = 41° 24'; 
the horizontal angle GAB =96° 28', and the angle of eleva- 
tion DBO= 10°43'. 

In the triangle BOA, to find the horizontal distance BO. 
The angle BOA = 180° - (41° 24' + 96° 28') = 42° 08' = 0. 

As sin 42° 08' ar. comp. 0.173369 

sin J. 96° 28' . 9.997228 

AB 780 2.892095 



BO 1155.29 3.062692. 



SEC. Ill] PLANE TRIGONOMETRY. 57 

In the right-angled triangle DBG, to find DC. 

As B ar. comp. 0.000000 

ta.n DBG 10° 43' 9.277043 

BG 1155.29 3.062692 



DC 218.64 2.339735. 



Eemark I. It might, at first, appear, that the solution 
which we have given, requires that the points B and A 
should be in the same horizontal plane ; but it is entirely 
independent of such a supposition. 

For, the horizontal distance, which is represented by 
BA, is the same, whether the station A is on the same 
level with B, above it, or below it. The horizontal angles 
GAB and GBA are also the same, so long as the point G 
is in the vertical line DG. Therefore, if the horizontal 
line through A should cut the vertical line DG, at any 
point, as U, above or below C, AB would still be the hori- 
zontal distance between B and A, and AU, which is equal 
to A G, would be the horizontal distance between A and G. 

If at A, we measure the angle of elevation of the point 
D, we shall know in the right-angled triangle DAB, the 
base AB, and the angle at the base; from which the per- 
pendicular DB can be determined. 

37. Let us suppose that we had measured the angle of 
elevation DAB, and found it equal to 20° 15'. 

First : In the triangle BA C, to find AG or its equal AB. 

As sin G 42° 08' ar. comp. 0.173369 

sin ^ 41° 24' 9.820406 

AB 780 2.892095 



AG 768.9 2.885870. 



In the right-angled triangle DAB, to find DB. 

3 B ar. comp. 0.000000 

tan J. 20° 15' 9.566932 

AB 768.9 2.885870 



DB 283.66 . 2.452802. 




68 ELEMENTS OF SURVEYING. [BOOK I. 

Now, since BO is less tlian 
B^, it follows that the station B 
is above the station A. That is, 

BB- BC= 283.66 - 218.64 = 
65.02 = BC, 
which expresses the vertical dis- 
tance that the station B is above 
the station A. 

Eemark II. It should be remembered, that the vertical 
distance which is obtained by the calculation, is estimated 
from a horizontal line passing through the eye at the time 
of observation. Hence, the height of the instrument is to 
be added, in order to obtain the true result. 



SECOND METHOD. 

88. When the nature of the ground will admit of it, 
measure a base line AB in the direction of the object B. 
Then measure with the instrument the angles of elevation 
at A and B. 

Then, since the out- 
ward angle BBC is 
equal to the ^um of 
the angles A and ABB, 
it follows that the an- j?!^^^^^^^s^^ 
gle ABB is equal to the difference of the angles of eleva- 
tion at A and B. Hence, we can find all the parts of the 
triangle ABB. Having found BB, and knowing the angle 
BBC, we can find the altitude BC. 

This method supposes that the stations A and B are on 
the same horizontal plane ; and therefore it can only be 
used when the line AB is nearly horizontal. 

Let us suppose that we have measured the base line, 
and the two angles of elevation, and 

(AB =975 yards, 
found J ^ =15° 86', 
[BBC = 27° 29'; 

required the altitude BC. 




SEC. Ill] PLANE TRIGONOMETRY. 59 

First : ADB= DBC - ^ = 27° 29' - 15° 36' - 11° 53'. 
In the triangle ADB, to find BD. 



As sin J) 
: sin A 
:: AB 


11° 53' ar. comp. 

15° 36' 

975 

1273.3 


0.686302 
9.429623 
2.989005 


DB 


■ 3.104930. 




the triangle DBG, to find DG. 

ar. comp. 

27° 29' 

1273 3 




In 

As R 

: sin B 

DB 


0.000000 
9.664163 
3.104930 




687.61 




: DG 


2.769093. 



III. To determine the perpendicular distance of an object helow 
a given horizontal plane. 

39. Suppose G to be directly 
over tlie given object, and A the 
point through, which the horizon- 
tal plane is supposed to pass. 

Measure a horizontal base line 
AB, and at the stations A and 
B conceive the two horizontal 
lines AG, BG, to be drawn. The 
oblique lines from A and B to the object are the hy- 
pothenuses of two right-angled triangles, of which AG, BG, 
are the bases. The perpendiculars of these triangles are 
the distances from the horizontal lines A G, BG, to the 
object. If we turn the triangles about their bases AG, 
BG, until they become horizontal, the object, in the first 
case, will fall at G', and in the second at G". 

Measure the horizontal angles GAB, GBA, and also the 
angles of depression G'AG, G"BG. 




60 ELEMENTS OF SURVEYING. 

Let US suppose tliat we liave 

" AB =672 yards 

BAG =72° 29' 

found i ABG = 89° 20' 

C'AO = 27° 49' 

^ C"BC= 19° 10'. 

First: in tlie triangle ABC, 
ihe^ horizontal angle ACB= 180" 
49' = 68° 11'. 



[BOOK I. 



(^+5)=i8o°-iir 



To find the horizontal distance A 0. 

As sin 68° 11' ar. comp. 0.032275 

sin ^ 39° 20' 9.801973 

AB 672 2.827369 

AC 458.79 ........ 2.661617. 



To find the horizontal distance BC. 

As sin G %8° 11' ar. comp. 0.032275 

sin ^ 72° 29' 9.979380 

AB 672 2.827369 

BG 690.28 2.839024. 



In the triangle GA G\ to find GG'. 

As R ar. comp. 0.000000 

tan C'^C 27° 49' 9.722315 

AG 458.79 2.661617 

GC' 242.06 2.383932. 



In the triangle GBG'\ to find GG". 

As R ar. comp. 0.000000 

tan G"BG 19° 10' 9.541061 

BG 690.28 2.839024 

GG" 239.93 2.380085. 



Hence also, GG' - GG" = 242.06 - 239.93 = 2.13 yards, 
wliicli is the height of the station A above station B. 



SEC. Ill] 



PLANE TRIGONOMETRY. 



61 




PROBLEMS. 

1. "Wanting to know tlie distance between two inacces- 
sible objects, wbicli lie in a direct level line from the bot- 
tom of a tower of 120 feet in height, the angles of depres- 
sion are measured from the top of the tower, and are found 
to be, of the nearer 57°, of the more remote 25° 30' : re- 
quired the distance between the objects. 

A71S. 173.656 feet. 

2. In order to find the distance 
between two trees, A and B, which 
could not be directly measured be- 
cause of a pool which occupied the 
intermediate space, the distances 
of a third point from each of 
them were measured, and also the 
included angle ACB: it was found that, 

CB =672 yards, 
GA =588 yards, 
^CS = 55°40'; 
required the distance AB. Ans. 592.967 yards. 

3. Being on a horizontal plane, and wanting to ascer- 
tain the height of a tower, standing on the top of an in- 
accessible hill, there were measured, the angle of elevation 
of the top of the hill 40°, and of the top of the tower 51° ; 
then measuring in a direct line 180 feet farther from the 
hill, the angle of elevation of the top of the tower was 
33° 45' ; required the height of the tower. 

Ans. 83.998. 

4. Wanting to know the hori- 
zontal distance between two inac- 
cessible objects B and W, the fol- 
lowing measurements were made. ^^^^^^^g 

AB =536 yards 
BAW=4:0°16' 
WAB= 57° 4:0' 
ABB =42° 22' 
BBW= 71° 07'] 
required the distance BW. Ans. 939.527 yards. 




j62 



ELEMENTS OF SURVEYI^-G. 



[BOOK I 




5. Wanting to know the 
horizontal distance between 
two inacessible objects A 
and B, and not finding any 
station from which both of 
them could be seen, two 
points C and Z>, were chosen 
at a distance from each other, equal to 200 yards ; from 
the former of these points A could be seen, and from the 
latter B, and at each of the points C and I) a staff was 
set up. From a distance CF was measured, not in the 
direction BG, equal to 200 yards, and from B a distance 
BB equal to 200 yards, and the following angles taken, 

r AFC = 83° 00', BBE = 54° 30', 
viz. ]aCB-= 53° 30', BBC ^ 156° 25', 
[ACF = 54° 31', BEB = 88° 30'. 

Ans. AB=S4:5A67 yards. 



6. From a station P there 
can be seen three objects. A, 
B and (7, whose distances from 
each other are known : viz., 
AB--= 800, AC= 600, and BO 
= 400 yards. Now, there are 
measured the horizontal an- 
gles. 

APC=?>%° 45' and BPC 
= 22° 30': it is required to 
find the three distances PA, PC, and PB. 




P ~ 



r PA = 710.193 yards. 
Ans. ipC = 1042.522 
[p^ = 934.291. 



7. This problem is much used in maritime survey- 
ing, for the purpose of locating buoys and sounding boats. 
The trigonometrical solution is somewhat tedious, but it 
may be solved geometrically by the following easy con- 
struction. 



SEC. III.] 



PLANE TRIGONOMETRY. 



63 



Let A, B, and G be the 
three fixed points on shore, 
and P the position of the 
boat from which the angles 
APO= 33° 45', GPB= 22° 30', 
and APB=6Q° 15', have been 
measured. 

Subtract twice APC=Q1° 
30' from 180°, and lay off at 
A and C two angles, GAO^ 
A GO^ each equal to half the 
remainder =56° 15'. With 
the point 0, thus determined, 
as a centre, and OA or OC as a radius, describe the cir- 
cumference of a circle : then, any angle inscribed in the 
segment APG^ will be equal to 33° 45'. 

Subtract, in like manner, twice GPB=4:5°, from 180°, 
and lay off half the remainder = 67° 30', at B and G, de- 
termining the centre ^ of a second circle, upon the cir- 
cumference of which the point P will be found. The 
required point P will be at the intersection of these two 
circumferences. If the point P fall on the circumference 
described through the three points A, B, and (7, the two 
auxiliary circles will coincide, and the problem will be in- 
determinate. 




BOOK II. 

PLANE SUEYEYING. 



SECTION I. 

DEFINITIONS. — MEASUKEMENT OP ANGLES AND LINES. 

1. Surveying-, in its most extensive signification, com- 
prises all tlie operations necessary for finding, 

1st. The area or contents of any portion of the surface 
of the earth ; 

2d. The lengths and directions of the bounding lines ; 
and, 

3d. For making accurate delineations of the surface and 
bounding lines on paper. 

It is divided into two branches, Plane and Geodesic 
Surveying. 

2. The radius of the earth being very large, the curva- 
ture may be neglected, when the survey is limited to small 
portions of the surface. This branch is called Plane Sur- 
veying. 

When the curvature is taken into account, as it must 
be in all extensive surveys, the method of measurement 
and computation is called Geodesic Surveying. 

8. If at any point of the surface of the earth, regarded 
as a sphere, a plane be passed perpendicular to the radius, 
it will be tangent to the surface. Such a plane, and all 
planes parallel to it, are called horizontal planes. 

4. A plane perpendicular to a horizontal plane, at a 
given point, is called a vertical plane. 




SEC. I] DEmfiTioifa. 65 

5. All lines of Korizontal planes are called horizontal 
lines. 

6. Lines "wMcli are perpendicular to a horizontal plane, 
are called vertical lines ; and all lines whicli are inclined to 
it, are called oblique lines. 

Thus, AB and DG are hori- jj^ 
zontal lines ; BG and AD are 
vertical lines ; and A G and BD 
are oblique lines. 

7. The horizontal distance 
between two points, is the horizontal line intercepted be- 
tween the two vertical lines passing through those points. 
Thus, X>(7 or AB is the horizontal distance between the two 
points A and (7, or the points B and D. 

8. A horizontal angle is one whose sides are horizontal; 
its plane is also horizontal. 

A horizontal angle may also be defined to be, the angle 
included between two vertical planes passing through the angular 
point, and the two objects which subtend the angle. 

9. A vertical angle is one, the plane of whose sides is 
vertical. 

10. An angle of elevation^ is a vertical angle having one 
of its sides horizontal, and the inclined side above the hor- 
izontal side. 

Thiis, in the last figure, BAG is the angle of elevation 
from A to O. 

11. An angle of depression^ is a vertical angle having 
one of its sides horizontal, and the inclined side under the 
horizontal side. Thus, JDGA is the angle of depression 
from G to A. 

12. An oblique angle is one, the plane of whose sides is 
oblique to a horizontal plane. 

13. All lines, which can be the object of measurement, 
must belong to one of the classes above named, viz. : 

1st. Horizontal lines : 
2d. Vertical lines : 
3d. Oblique lines. 



66 ELEMENTS OF SURVEYING. [BOOK 11. 

14. All the angles may also be divided into three 
classes, viz. : 

1st. Horizontal angles : 

2d. Vertical angles ; which, include angles of elevation 
and angles of depression : and 

3d. Oblique angles, or those included by oblique lines. 



OF THE MEASUREMENT OF LINES AND ANGLES. 

15. It has been shown (Bk. I., Sec. III., Art. 1), that at 
least one side and two of the other parts of a plane triangle 
must be given or known, before the remaining parts can 
be found by calculation. 

When, therefore, distances are to be found, by trigono- 
metrical calculations, two preliminary steps are necessary : 

• 1st. To measure certain lines on the ground : 
2d. To measure such angles as may be necessary to de- 
termine the required parts. 



MEASURES FOR DISTANCES. 

16. Any tape, rod, or chain, divided into equal parts, 
may be used as a measure ; and one of these equal parts 
is called the unit of the measure. The unit of a measure 
may be a foot, a yard, a rod, or any other ascertained 
distance. 

The measure in general use, is a chain of four rods or 
sixty-six feet in length ; it is called Gunter's chain, from 
the name of the inventor. This chain is composed of 100 
links. Every tenth link from either end, is marked by a 
small attached brass plate, which is notched, to designate 
its number from the end. The division of the chain into 
100 equal parts, is a very convenient one, since the divi- 
sions or links are decimals of the whole chain, and in the 
calculations may be treated as such. 



SEC. I] MEASUREMENT OF DISTANCES. 67 

TABLE. 

1 chain = 4 rods = 66 feet = 792 inclies = 100 links. 
Hence, 1 link is equal to 7.92 inches. 
80 chains = 320 rods = 1 mile. 
40 chains = | mile. 
20 chains =.^ mile. 

17. Besides the chain, there are needed for measuring, 
ten marking pins, which should be of iron, each about ten 
inches in length and an eighth of an inch in thickness. 
These pins should be strung upon an iron ring, and this 
ring should be attached to a belt, to be passed over the 
right shoulder, suspending the pins at the left side. Two 
staves are also required. Each of these should be about six 
feet in length, and have a spike in the lower end to aid in 
holding it firmly, and a horizontal strip of iron to pre- 
vent the chain from slipping off; these staves are to be 
passed through the rings at the ends of the chain. 

TO MEASURE A HORIZONTAL LINE. 

18. At the point where the measurement is to be be- 
gun, place, in a vertical position, a signal staff, having a 
small flag attached to its upper extremity ; and place an- 
other at the point where the measurement is to be termi- 
nated. These two points are generally called stations. 

Having passed the staves through the rings of the 
chain, let the ten marking pins and one end of the chain 
be taken by the person who is to go forward, and who is 
called the leader, and let him plant the staff as nearly as 
possible in the direction of the stations. Then, taking the 
staff in ,his right hand, let him stand off at arm's length, 
so that the person at the other end of the chain can align 
it exactly with the stations : when the alignment is made, 
let the chain be stretched and a marking pin placed ; then 
measure a second chain in the same manner, and so on, 
until all the marking pins shall have been placed. When 
the marking pins are exhausted, a note should be made, 
that ten chains have been measured ; after which, the 
marking pins are to be returned to the leader, and the 



68 



ELEMENTS OF SUKVEYIN-Q. [BOOK IL 



measurement continued as before, until the wliole distance 
is passed over. It will be found desirable to fasten pieces 
of red cloth, to the heads of the marking pins, that they 
may be more readily found in thick grass, brushwood, &c. 

Great care must be taken to keep the chain horizontal, 
and if the slope of the ground be too great to admit of 
measuring a whole chain at a time, a part of a chain only 
should be measured: the sum of all the horizontal lines so 
measured, is evidently the horizontal distance between the 
stations. 

For example, in measuring 
the horizontal distance between 
A and C, we first place a staff 
at A and another at b, in the 
direction towards 0. Then 
slide up the chain on the staff 
at A until it becomes horizon- 
tal, and note the distance ah. 
Then remove the staves and place them at b and d : make 
the chain horizontal, and note the distance cd. Measure 
in the same manner the line fC; the sum of the horizontal 
lines ab, cd, fC, is equal to AB, the horizontal distance be- 
tween A and C. 




19. The length of the chain should be compared, from 
time to time, with a standard kept for the purpose. 

To facilitate this comparison, let two stakes be driven 
in the ground, distant from each other one chain, and let 
nails be driven in the heads of the stakes to mark the ex- 
act length of the standard. 

Marks made upon the coping of a wall will answer the 
same purpose. If it is found that any line has been mea- 
sured with a chain, either too short or too long, the mea- 
sured distance may be corrected by the following pro- 
portion : 

As the length of the chain 
the length of the standard 
the measured distance 
the true distance. 



SEC. I] OF THE THEODOLITE. 

For the correction of areas we have this proportion, 
As the square of the length of the chain 
the square of the length of the standard, 
the area found 
the area required. 



MEASUREMENT OF ANGLES. 

20. We come now to the measurement of angles, and 
for this purpose several instruments are used. The one, 
however, which affords the most accurate results, and which 
indeed can alone be relied on for nice or extensive opera- 
tions, is called a Theodolite. This instrument only will be 
described at present ; others will be subsequently explained. 



OF THE THEODOLITE. 

PI. 1. The theodolite is an instrument used to measure 
horizontal and vertical angles. It is usually placed on a 
tripod ABQ which enters by means of a screw the lower 
horizontal plate DJBJ^ and becomes firmly attached to the 
body of the instrument. Through the horizontal plate BU, 
four small hollow cylinders are inserted, which receive 
four screws with milled heads, that work against a second 
horizontal plate, FQ. The upper side of the plate BJE 
terminates in a curved surface, which encompasses a ball, 
that is nearly a semi-sphere, with the plane of its base 
horizontal. This ball, which is hollow, is firmly connected 
with the smaller base of a hollow conic frustum, that 
passes through the curved part of the plate DJS, and 
screws firmly into the curved part of the second horizontal 
plate FG. 

A hollow conic spindle passes through the middle of 
the ball, and the hollow frustum with which it is connect- 
ed. To this spindle, a third horiz;ontal and circular plate 
HI, called the limb of the instrument, is permanently attached. 
Within this spindle, and concentric with it, there is a sec- 
ond spindle, called the inner, or solid spindle. To this 
latter, is united a thin circular plate, called the vernier plate, 



70 ELEMENTS OF SURVEYING. [BOOK II. 

wliicli rests on tlie limb of the instrument, and supports 
the upper frame- work. The two spindles terminate at the 
base of the spherical ball, where a small screw enters the 
inner one, and presses a washer against the other, and the 
base of the ball. On the upper surface of the plate FG, 
rests a clamp which goes round the outer spindle, and 
which, being compressed by the clamp-screw K^ is made 
fast to it. This clamp is thus connected with the plate 
FQ. A small cylinder a, is fastened to the plate FG : 
through this cylinder a thumb-screw L passes, and works 
into a small cylinder i, connected with the clamp. The 
cylinders h and a, admit of a motion round their axes, to 
relieve the screw L of the pressure which would otherwise 
be occasioned by working it. 

Directly above the clamp, is the lower telescope MK 
This telescope is connected with a hollow cylinder, which 
is worked freely round the outer spindle, by the thumb- 
screw P having a pinion working into a concealed cog- 
wheel, that is permanently fastened to the limb of the in- 
strument. By means of a clamp-screw Q^ the telescope is 
made fast to the limb, when it will have a common motion 
with the limb and outer spindle. 

The circular edge of the limb is chamfered, and is gen- 
erally made of silver, and on this circle the graduation for 
horizontal angles is made. In the instrument described, 
the circle is cut into degrees and half degrees ; the degrees 
are numbered from to 360. 

On the circular edge of the vernier plate, is a small 
plate of silver, called a vernier ; this plate is divided into 
30 equal parts, and numbered from the line marked to 
the left. Two levels, at right angles to each other, are 
attached to the vernier plate by small adjusting screws ; 
one of the levels is seen in the figure. 

The vernier plate turns freely around with the inner 
spindle. It is made fast to the limb of the instrument by 
the clamp-screw S] after which the smaller motions are 
made by the tangent-screw T. There is a compass on the 
vernier plate, that is concentric with it, the use of which 
•will be explained under the head compass. 



SEC. I.] OF THE THEODOLITE. 71 

The frame-work wliich supports the horizontal axis of 
the vertical semicircle UV and the upper telescope, with 
its attached level, rests on the vernier plate, to which it 
is made fast bj three adjusting screws, placed at the angu- 
lar points of an equilateral triangle. The vertical semi- 
circle UV, is called the vertical limb ; its motions are gov- 
erned by the thumb-screw Z, which has a pinion, that 
works with the teeth of the vertical limb. On the face 
of the vertical limb, opposite the thumb-screw Z, the limb 
is divided into degrees and half degrees : the degrees are 
numbered both ways from the line marked 0. There is a 
small plate resting against the graduated face of the verti- 
cal limb, called the vernier ; it is divided into 30 equal 
parts, and the middle line is designated by 0. 

On the other face of the vertical limb, are two ranges 
of divisions, commencing at the point, and extending 
each way 45°. The one shows the vertical distance of 
any object to which the upper telescope is directed, above 
or below the place of the instrument, in 100th parts of the 
horizontal distance: the other, the difference between the 
hypothenusal and base lines : the hypothenuse being sup- 
posed to be divided into one hundred equal parts : there- 
fore, by mere inspection, we can ascertain the number of 
links, which must be subtracted from every chain of an 
oblique line, to reduce it to a true horizontal distance. 

The supports of the upper telescope are called the 
wyes, and designated ys. Two loops, turning on hinges, 
pass over the telescope, and are made fast by the pins c 
and d] these loops confine the telescope in the F's. By 
withdrawing the pins, and turnilig the loops on their 
hinges, the telescope may be removed for the purpose of 
being reversed in position ; and in both situations, the tele- 
scope can be revolved in the F'5 about its axis. 

In the telescopes attached to the theodolite, are two 
principal lenses, one at each end. The one at the end 
where the eye is placed, is called the eye-glass, the other 
the object-glass. 

In order that the axis of the telescope may be directed 
to an object with precision, two spider's lines, or small 



72 ELEMENTS OF SURVEYIJfG. [BOOK 11. 

hairs, are fixed at riglit angles to eacli other, and placed 
within the barrel of the telescope, and at the focus of the 
eye-glass. The vertical hair is moved by two small hori- 
zontal screws, one of which, / is seen in the figure ; and 
the horizontal hair, by two vertical screws, g and h. 

Before using the instrument it must be adjusted, that is, 
the parts must be brought to their proper relative positions : 
there are four principal adjustments. 

First adjustment. — To fix the intersection of the spider'a 
lines in the line of collimation or axis of the telescope. 

Having screwed the tripod to the instrument, extend 
the legs, and place them firmly. Then loosen the clamp- 
screw S of the vernier plate, and direct the telescope to a 
small, well-defined, and distant object. By means of a 
small pin t, on the under side of the telescope, slide the 
eye-glass till the spider's lines are seen distinctly ; then with 
the thumb-screw X, which forces out and draws in, the 
object-glass, adjust this glass to its proper focus, when the 
object, as well as the spider's lines, will be distinctly seen : 
after which, by the tangent-screw T and the thumb-screw 
Z, bring the intersection of the spider's lines exactly upon 
a well-defined point of the object. 

Having done this, revolve the telescope in the Yh half 
round, when the attached level mn, will come to the upper 
side. See, in this position, if the horizontal hair appears 
above or below the point, and in either case, loosen one, 
and tighten the other, of the two screws that work the 
horizontal hair, till the horizontal hair has been carried 
over half the space between its last position and the ob- 
served point. Carry the telescope back to its place ; di- 
rect again the intersection of the spider's lines to the point, 
and repeat the operation till the horizontal hair neither 
ascends nor descends, while the telescope is revolved. A 
similar process will arrange the vertical hair, and the line 
of collimation is then adjusted. 

Second adjustment. — To make the axis of the attached 
level of the upper telescope, parallel to the line of collimation. 

Turn the vernier plate, till the telescope comes directly 



SEC. I.] OF THE THEODOLITE. 73 

over two of tlie levelling screws, between the plates DE 
and FG. Turn these screws contrary ways, keeping them 
firm against the plate FG^ till the bubble of the level mn, 
stands at the middle of the tube. Then, open the loops, 
and reverse the telescope. If the bubble still stands in the 
middle of the tube, the axis of the tube is horizontal ; but 
if not, it is inclined, the bubble being at the elevated end. 
In that case, by means of the small vertical screws m and 
n, at the ends of the level, raise the depressed end, or de- 
press the elevated one, half the inclination ; and then, with 
the levelling screws, bring the level into a horizontal posi- 
tion. Eeverse the telescope in the Y's^ and make the 
same correction again ; and so on, until the bubble stands 
in the middle of the tube, in both positions of the tele- 
scope : the axis of the level is then horizontal. Let the 
telescope be now revolved in the y's. If the bubble con- 
tinue in the middle of the tube, the axis of the level is 
not only horizontal, but also parallel to the line of coUi- 
mation. If, however, the bubble recede from its centre, 
the axis of the level is inclined to the line of collimation, 
and must be made parallel to it by means of two small 
antagonistic screws, (one of which is seen at p,) which work 
horizontally. By loosening one of them, and tightening 
the other, the level is soon brought parallel to the line of 
collimation, and then, if the telescope be revolved in the 
F's, the bubble will continue in the middle of the tube. 

It is difficult to make the first part of this adjustment, 
while the axis of the level is considerably inclined to the 
line of collimation ; for, if the level were truly horizontal 
in one position of the telescope, when the telescope is re- 
versed, the bubble would not stand in the middle of the 
tube, except in one position of the level. This suggests 
the necessity of making the first part of the adjustment 
with tolerable accuracy ; then, having made the second 
with care, let the first be examined, and proceed thus till 
the adjustment is completed. 

Third adjustment. — To make the axes of the levels on 
the limb perpendicular to the axis of the instrument. 

This adjustment is effected, partly by the levelling 



74 ELEMENTS OF SURVEYING. [BOOK II. 

screws, and partly by tlie thumb-screw Z. Turn the ver- 
nier plate, until the upper telescope •comes directly over 
two of the levelling screws, then turn them contrary ways, 
till the upper telescope is horizontal; after which, turn the 
vernier plate 180°, and if the bubble of the level remains 
in the middle of the tube, one line of the limb is horizon- 
tal. But if the bubble recede from the centre of the level, 
raise the lower, or depress the upper end, one -half by the 
levelling screws, the other by the thumb-screw Z^ till it is 
brought into a horizontal position. Turn the vernier plate 
again 180°, and if the level be not then horizontal, make 
it so, by dividing the error as before, and repeat the op- 
eration until the line of the limb is truly horizontal. 
Then turn the vernier plate 90°, and level as before. 
The limb ought now to be truly horizontal ; but lest the 
first horizontal line may have been changed, in obtaining 
the second, it is well to bring the telescope and level two 
or three times over the levelling screws, until an entire 
revolution can be made without displacing the bubble from 
the middle of the tube. As this can only be the case 
when the level revolves around a vertical line, it follows 
that the limb will then be horizontal, and the axis of the 
instrument vertical, and hence, the axes of the levels will 
be perpendicular to the axis of the instrument. 

Fourth adjustment, — To make the axis of the vertical 
limb perpendicular to the axis of the instrument 

Bring the intersection of the spider's lines of the upper 
telescope upon a plumb line, or any well-defined vertical 
object, and move the telescope with the thumb-screw Z: 
if the intersection of the spider's lines continue on the ver- 
tical line, the axis is horizontal. 

Or, the adjustment may be effected thus : Direct the 
intersection of the spider's lines to a well-defined point 
that is considerably elevated : then turn the vertical limb, 
until the axis of the telescope rests on some other well-de- 
fined point, upon or near the ground : reverse the tele- 
scope, and turn the vernier plate 180° ; now, if in elevating 
and depressing the telescope, the line of coUimation passes 



SEC. I.] VERNIERS. 75 

througli the two points before noted, tlie axis is horizontal. 
If it be found, by either of the above methods, that the 
axis is not horizontal, it must be made so by the screws 
which fasten the frame-work to the vernier plate. 

There are two important lines of the theodolite, the po- 
sitions of which, are determined with great care by the 
maker, and fixed permanently. First, the axis of the in- 
strument is placed exactly at right angles with the limb 
and vernier plate ; and unless it have this position, the 
vernier plate will not revolve at right angles to the axis, 
as explained in the third adjustment. Secondly, the line 
of collimation of the upper telescope is fixed at right angles 
to the horizontal axis of the vertical limb. We can as- 
certain whether these last lines are truly at right angles, 
by directing the intersection of the spider's lines to a well- 
defined j)oint ; then removing the caps which confine the 
horizontal axis in its supports, and reversing the axis : if 
the intersection of the spider's lines can be made to cover 
exactly the same point, without moving the vernier plate, 
the line of collimation is at right angles to the axis. 

K the theodolite be so constructed that either of the 
y's admits of being moved laterally, so as to vary the 
angle between the horizontal axis and the line of collima- 
tion, these lines may be adjusted at right angles to each 
other, if they have not been so placed by the maker. 

The lower telescope being used merely as a guard, re- 
quires no adjustment, although it is better to make the 
axis, about which its vertical motions are performed, hori- 
zontal, or perpendicular to the axis of the instrument ; and 
this is easily effected by means of the two small screws k 
und Z, which work into the slide J.', that is connected with 
the horizontal axis. 

Having explained the methods of properly adjusting the 
theodolite, we will now explain the particular uses of its 
several parts, and the manner of measuring 



VERNIERS. 

21. Before explaining the vernier, as applied to the the- 
odolite, we shall discuss the general theory of verniers. 



Y6 ELEMENTS OF SURVEYING. [BOOK 11. 

A Yernier is a contrivance for measuring parts of the 
equal spaces marked off on a given scale or limb. 

It is a graduated scale, so arranged, as to cover an ex- 
act number of equal spaces on the primary scale or liimh, 
to wMch. it is applied. It is divided into a ■ number of 
equal parts, greater by one tban tbe number of equal spaces 
which it covers on the hmb. 

The vernier may be applied to any scale of equal parts. 
The modes of its application are extremely various ; the 
principle, however, is the same in all, and may be illus- 
trated by a simple diagram. 

& 9 iO i1 fa 13 14- 1J Iff 17 18 
a\ I I \ \ B 



C I ^ 



Let AB be any Iwib or scale of equal parts, one of 
which let us suppose equal to h. Let GD be a vernier^ 
equal in length to nine of these parts, and itself divided 
into ten equal spaces, each one of which is then equal to 
nine-tenths of h. The difference between a space on the 
limb and a space on the vernier, is therefore equal to one- 
tenth of h or x^o&. This is the least space that can be meas- 
ured by means of the vernier, and is called the hast count; 
hence, 

The least count of a vernier is equal to one of the equal 
divisions of the limb divided hy the number of spaces on the 
vernier. 

22. The true reading of the instrument, for any position 
of the vernier, expresses the distance from the point where 
the graduation on the limb begins, marked 0, to the 
point of the vernier. In the diagram, that distance is ex- 
pressed by nine units of the scale, or 9. 

If, now, the vernier be moved till the division 1 coin- 
cides with the division 10 of the hmb, the point will 
have advanced along the limb a distance equal to j^S, 
and the reading will become 9 + ^^b. If we again 
move the vernier till the division 2 coincides with the di- 
vision 11 of the scale, the point will have advanced an 
additional distance, equal to ^b, and the reading becomes 



SEC. L] MEASUREMENT OF ANGLES. 77 

9 + ^ob ; wlieii 3 coincides witli division 12, the reading 
will become 9 + x^o^, and so on, till finally, when the point 

10 coincides with 19 of the sc^^le, the distance 9 will have 
been increased bj \%h^ and will become 10, as it should, 
since, in that case, the point will have been moved a whole 
space, and will coincide with the division 10 of the limb. 
Hence, the following rule for reading an instrument which 
has a vernier. 

Read the limb in the direction of the graduation up to the 
division line next 'preceding the point of the vernier ; this 
is called the reading on the limb. Look along the vernier till 
a dividing line is found to coincide with a line of the limb : 
multiply the number of this first line by the least count of the ver- 
nier : this is the reading on the vernier: the sum of these two 
readings is the reading of the instrument. 

23. In the theodolite described, the limb is divided into 
half degrees, and 30 spaces on the vernier cover 29 spaces 
on the limb. Hence, the least count of this instrument is 
^ of a half degree or 1'. Fig, 2, Plate 1, exhibits the 
vernier of the horizontal limb, and Fig. 3 the vernier of 
the vertical limb. 



TO MEASUEE A HORIZONTAL ANGLE WITH THE THEODOLITE. 

24. Place the axis of the instrument directly over the 
point at which the angle is to be measured. This is ef- 
fected by means of a plumb, suspended from the plate 
which forms the upper end of the tripod. 

Having made the limb truly level, place the of the 
vernier at or 360° of the limb, and fasten the clamp- 
screw S of the vernier plate. Then, facing in the direc- 
tion between the lines which subtend the angle to be mea- 
sured, turn the limb with the outer spindle, until the tele- 
scope points to the object on the left, very nearly. Clamp 
the limb with the clamp-screw -S", and by means of the 
tangent screws L and Z, bring the intersection of the 
spider's lines to coincide exactly with the object. 

Having loosened the clamp-screw Q of the lower tele- 
scope MN^ direct it with the thumb-screw P to the 



78 ELEMENTS OF SURVEYING. [BOOK II. 

same object at whicli the upper telescope is directed ; then 
tighten tlie clamp-screw Q. This being done, loosen the 
clamp-screw S of the vernier plate, and direct the telescope 
to the other object : the arc passed over by the point 
of the vernier, is the measure of the angle sought. 

The lower telescope having been made fast to the limb, 
will indicate any change of the position of the limb, should 
any have taken place ; and, as the accuracy of the mea- 
surements depends on the fixedness of the limb, the lower 
telescope ought to be often examined, and if its position has 
been altered, the limb must be brought back to its place by 
the tangent-screw L. 

It is not necessary to place the point of the vernier 
at the point of the limb, previously to^ commencing the 
measurement of the angle, but convenient merely ; for, 
whatever be the position of this point on the limb, it is 
evident that the arc which it passes over is the true mea- 
sure of the horizontal angle. If, therefore, its place be 
carefully noted for the first direction, and also for the sec- 
ond, the difference of these two readings will be the true 
angle, unless the point of the vernier shall have passed 
the point of the limb, in which case the greater reading 
must be subtracted from 860°, and the remainder added to 
the less. 



TO MEASURE A VERTICAL ANGLE. 

25. We shall first explain the method of determining 
the index error. Having levelled the horizontal limb, di- 
rect the telescope to some distinctly marked object as the 
top of a chimney, and read the instrument. Reverse the 
telescope in the Y^s^ and turn the vernier plate»180°, and 
having directed the telescope to the same object, again 
read the instrument. If the two readings are the same, 
the limb is adjusted ; that is, the of the limb coincides 
with the of its vernier, when the axis of the telescope 
is parallel to the horizontal limb. 

When the reading found with the eye end of the tele- 
scope nearest the vernier, is greater than that obtained in 
the reversed position, the true elevation of the object 



SEC. I] PRACTICAL PROBLEMS. 79 

whicli is equal to a mean of tlie readings, may be obtained 
bj subtracting half their difference from the first reading. 
If the first reading is less than the second, the half differ- 
ence must be added to the first. Hence, 

To find the index error^ take the reading of the limb ivhen 
the telescope is directed to a fixed object, first with the eye end 
of the telescope nearest the vernier, and then ivith the telescope 
and vernier plate both reversed. Take half the difference of 
these readings, and affect it with a minus sign if the first is 
greater, or a plus sign if the second is the greater ; this is equal 
to the index error. 

Let the operation be repeated several times, using dif- 
ferent objects, and a mean of the errors will be more cor- 
rect than the result of a single observation. 

26. Having determined the index error, let the axis of 
the telescope be directed to any point either above or be- 
low the plane of the limb, and read the arc indicated by 
the of the vernier. To the arc so read apply the proper 
correction, if any, and the result will be the true angle of 
elevation or depression. 

The angle of elevation may be more correctly foimd by 
taking the elevation of the object, and repeating the obser- 
vation with the telescope and vernier plate reversed, and 
then taking a mean of the readings for the angle required. 

MEASUREMENTS WITH THE TAPE OR CHAIN ONLY. 

27. It often happens that instruments for the measur- 
ment of angles cannot be easily obtained ; we must then 
rely entirely on the tape or chain. 

We now propose to explain the best methods of deter- 
mining distances, without the aid of instruments for the 
measurement of horizontal or vertical angles. 

I. To trace, on the ground, the direction of a right line, that 
shall be perpendicular at a given point, to a given right 
line. 

FIRST METHOD. 

28. Let BG be the given right line, and A the given 



80 



ELEMENTS OF SURVEYING. [BOOK IL 



point. Measure from A, on tlie 
line BC, two equal distances AB, 
AC, one on each side of tlie point 

A. Take a portion of the chain ^ 

or tape, greater than AB, and B jl C 

place one extremity at B, and with the other trace the arc 
of a circle on the ground. Then remove the end which 
was at B, to 0, and trace a second arc intersecting the 
former at I). The straight line drawn through B and A 
will be perpendicular to BC at A. 



SECOND METHOD. 

29. Having made AB= A C, take 
any portion of the tape or chain 
considerably greater than the dis- 
tance between B and 0. Mark 
the middle point of it, and fasten 
its two extremities, the one at B 
and the other at 0. Then, taking the chain by the middle 
point, stretch it tightly on either side of BC, and place a 
staff at B or JE: BAB will be the perpendicular re- 
quired. 




/\ 



THIRD METHOD. 

80. Let AB be the given line, 
and C the point at which the per- 
pendicular is to be drawn. From 
the point C measure a distance CA A— 
equal to 8. With C as a centre, 
and a radius equal to 6, describe 
an arc on either side of AB : then, 
with J. as a centre, and a radius equal to 10, describe a 
second arc intersecting at E, the one before described : 
then draw the line EC, and it will be perpendicular to 
AB at a 

Eemark. Any three lines, having the ratio of 6, 8, and 
10, form a right-angled triangle, of which the side corre- 
sponding to 10 is the hypothenuse. 



I 



SEC. I] SURVEYING CROSS. 81 



FOURTH METHOD. 



31. Let AD be tlie given riglit 
line, and D the point at which, 
the perpendicular is to be drawn. jf 

Take any distance on the tape ^ ^„.^-^ 
or chain, and place one extrem- -'^\ 
ity at i), and fasten the other 
at some point, as E^ between 




the two lines which are to form the right angle. Place a 
staff at E. Then, having stationed a person at i), remove 
the extremity of the chain and carry it round until it 
ranges on the line DA at A. Place a staff at A : then 
remove the end of the chain at A, . and carry it round 
until it falls on the line AE at E. Then place a staff at 
E; ADE will be a right angle, being an angle in a 

semicircle. 

•i 
32. There is a very simple instrument, used exclusively 
in laying off right angles on the ground, which is called 
the 

SURVETIKG CROSS. 

PI. 2, Fig. 1. This instrument consists of two bars, AB 
and OD, permanently fixed at right angles to each other, 
and firmly attached at ..£^ to a pointed staff, which serves 
as a support. Four sights are screwed firmly to the bars, 
by means of the screws a, 5, c, and d. 

As the only use of this instrument is to lay off right 
angles, it is of the first importance that the lines of sight 
be truly at right angles. To ascertain if they are so, let 
the bar AB be turned until its sights mark some distinct 
object ; then look through the other sights, and place a 
staff on the line which they indicate : let the cross be then 
turned until the sights of the bar AB come to the same 
line : if the other sights are directed to the first object, the 
lines of sight are exactly at right angles. 

The sights being at right angles, if one of them be 
turned in the direction of a given line,, the other will mark 
the direction of a hne perpendicular to it, at the point 
where the instrument is placed. . 



82 



ELEMENTS OF SURVEYING. [BOOK II. 



El 




n. From a given point without a straight line, to let fall a 
perpendicular on the line. 

83. Let C be tlie given point, and AB tlie given line. 

From C measure a line, as 
CA, to any point of the line AB. 
From A, measure on AB any 
distance as AF, and at F erect 
FF perpendicular to AB. ^^ ^' ^ .^ 

Having stationed a person at A, measure along tlie per- 
pendicular FF until the forward staff is aligned on the line 
AO: then measure the distance AF. Now, by similar tri- 
angles, we have, 

AF : AF :: AO : AB, 

in which all the terms are known except AB, which may, 
therefore, be found. The distance AB being laid off from 
A, the point B, at which the perpendicular CB meets AB, 
becomes known. If we wish the length of the perpen- 
dicular, we use the proportion, 

AF : FF :: AC : CB, 

in which all the terms are known, excepting CB: there- 
fore, CB may be determined. 



III. To determine the horizontal distance from a given point to 
an inaccessible object. 

FIRST METHOD. 

84. Let A be an inaccessible object, and F the point 
from which the distance is to be measured. 

At F lay off the right angle 
AFB, and measure in the di- 
rection FB, any convenient dis- 
tance to B, and place a staff 
at B. Then measure from F, 
directly towards the object A, 
a distance FB of a convenient 
length, and at B lay off a line 1> 
BC perpendicular to FA. Measure along the line BO, 



C 



l::i 



-E 



SEC. L] 



PRACTICAL PEOBLEMS. 



83 




■until a person at D shall range tlie forward staff on the 
line BA. Now, DF is known, being equal to the differ- 
ence between the two measured hues DB and GB. Hence, 
by similar triangles, 

BF : FG ■'. BE : FA, 

in which proportion all the terms are known, except the 
fourth, which may, therefore, be found. 

SECOND METHOD. 

35. At the point F lay off 
FB perpendicular to the line 
FA, and measure along it any 
convenient distance, as FB. 

At B lay off the right an- 
gle FBB, and measure any dis- 
tance in the direction BB. Let 
a person at B align a staff on 
BA, while a second person at B ahgns it on BF: the 
staff will thus be fixed at G. Then measure the dis- 
tance BG. 

The two triangles BGB and GAF being similar, we 
have, 

BG : BB :: GF : FA, 

in which all the terms are known, except the fourth, which 
may, therefore, be found. 

THIRD METHOD. 

36. Let B be the given point, and A the inaccessible 
object; it is required to find BA. 

Measure any horizontal base 
line, as BG. Then, having 
placed staves at B and G, 
measure any convenient dis- 
tances BB and GF, such that 
the points B, B, and A, shall 
be in the same right line, as 
also, the points F, G, and A ; 
then measure the diagonal lines 
BG and FB. 




84 



ELEMENTS OF SURVEYING. [BOOK II. 



Now, in tlie triangle BEG, 
tlie three sides are known, 
the^refore, tlie angle ECB can 
be found. In the triangle CDB, 
the three sides are also known, 
therefore the angle OBD can be 
determined. These angles be- 
ing respectively subtracted from 
180°, the two angles ACB and 
-4.5(7 become known ; and hence, 
in the triangle ABO^ we have two angles and the included 
side, to find the side BA. 




lY. To find the altitude of an ohject, when the distance to the 
vertical line passing through the top of it is known. 

87. Let CD be the altitude required, and A G the known 
distance. 

From A^ measure on 
the line AG^ any con- 
venient distance AB, and 
place a staff vertically 
at B. Then placing the 
eye at A, sight to the 
object D, and let the 
point, at which the line AD cuts the staff BE, be marked. 
Measure the distance BE on the staff; then. 




AB 



BE 



AG 



GD, 



whence CD becomes known. 

If the line AC cannot be measured, on account of in- 
tervening objects, it may be determined by calculation, as 
in the last problem, and then, having found the horizontal 
distance, the vertical line is readily determined, as before. 



SEC. IL] AREA OF LAND. 85 



SECTION II. 

AREA OR CONTENTS OF GROUND. — LAYING OUT LAJ^D. 

1. We come next to tlie determination of tlie area or 
superficial contents of ground. 

The surface of tlie ground being, in general, broken 
and uneven, it is impossible, without great trouble and ex- 
pense, to ascertain its exact area or contents. To avoid 
this inconvenience, it has been agreed to refer every sur- 
face to a horizontal plane : that is, to regard all its bound- 
ing lines as horLzontal, and its area as measured by that 
portion of the horizontal plane which the boundary lines 
enclose. 

For example, if ABCD were a 
piece of ground having an uneven 
surface, we should refer the whole 
to a horizontal plane, and take 
for the measure of the area that 
part of the plane which is inclu- 
ded between the bounding hori- 
zontal lines AB, BG, CD, DA. 

In estimating land in this manner, the sum of the areas 
of all the parts into which a tract may be divided, is equal 
to the area, estimating it as an entire piece : but this would 
not be the case if the areas of the parts had reference to 
the actual surface, and the area of the whole were calcu- 
lated from its bounding lines. 

2. The unit of measure of a quantity is a quantity of 
the same kind regarded as a standard, and with which all 
quantities of that kind may be compared. For lines, the 
unit is a right line of a known length, as 1 foot, 1 link, 1 
chain, or any other fixed distance. 

It has been already observed (Bk. II., Sec. L, Art. 16), 
that Gunter's chain of four rods or %& feet in length, and 
which is divided into 100 links, is the chain in general 




86 



ELEMEl^TS OF SURVEYING. [BOOK H 



use among surveyors. In measuring land, tlie length of 
this chain is generally taken for the unit of linear measure. 

3. The unit of measure for surfaces is a square de- 
scribed on the unit of linear measure. 



Thus, 1 square foot, 




1 square yard or 9 square feet. 



1 yard = 3 feet. 

















1 chain = 


= 4 rods. 



































1 square chain, or 16 square rods. 



When, therefore, the linear measures of ground are feet, 
yards, rods, or chains, the superficial measures are square 
feet, square yards, squ.are rods, or square chains ; and the 
numerical expression for the area is the number of times 
which the unit of superficial measure is contained in the 
land measured. 

4. An acre is a surface equivalent in extent to 10 square 
chains ; that is, equivalent to a rectangle of which one side 
is ten chains, and the other side one chain. 

One quarter of an acre is called a rood. 

Since the chain is 4 rods in length, 1 square chain eon- 
tains 16 square rods ; and therefore, an acre, which is 10 
square chains, contains 160 square rods, and a rood con- 
tains 40 square rods. The square rods are called 'perches. 

5. Land is generally computed in acres, roods, and 
perches, which are respectively designated by the letters 
A. B. P. 



SEC. 11] 



AREA OF LAND. 



87 



When tlie linear dimensions of a survey are cliains or 
links, the area will be expressed in square chains or square 
links, and it is necessary to form a rule for reducing this 
area to acres, roods, and perches. For this purpose, let us 
form the following 

TABLE. 



Miles. 


Acres. 


Eoods. 


Sq. Cliains. 


Perches. 


Sq. Links. 


1 


640 
1 


2560 
4 
1 


6400.0 

10.0 

2.5 

1.0 


102,400 

160 

40 

16 

1 


64,000,000 

100,000 

25,000 

10,000 

625 



1 square mile = 6400 square chains = 640 acres. 

Kow, when the linear dimensions are links, the area 
will be expressed in square links, and may be reduced to 
acres by dividing by 100000, the number of square links 
in an acre : that is, by pointing off five decimal places 
from the right hand. 

If the decimal part be then multiplied by 4, and five 
places of decimals pointed off from the right hand, the 
figures to the left will express the roods. 

If the decimal part of this result be now multiplied by 
40, and five places for decimals pointed off, as before, the 
figures to the left will express the perches. 

If one of the dimensions be in links, and the other in 
chains, the chains may be reduced to links by annexing 
two ciphers : or, the multiplication may be made without 
annexing the ciphers, and the product reduced to acres and 
decimals of an acre, by pointing off three decimal places 
from the right hand. 

When both the dimensions are in chains, the product 
is reduced to acres by dividing by 10, or pointing off one 
decimal place. 

From which we conclude; that, 

1st. If links he multiplied hy links, the product is reduced to 
acres hy pointing off Jive decimal places from the right hand. 



88 ELEMENTS OF SUEVEYING. [BOOK II. 

2d. If chains he multiplied by links, the product is reduced 
to acres by pointing off three decimal places from the right hand. 

8d. If chains be multiplied by chains, the product is reduced 
to acres by pointing off one decimal place from the right hand. 

6. Since there are 16.5 feet in a rod, a square rod is 
equal to . 16.5 X 16.5 = 272.25 square feet. 

If tlie last number be multiplied by 160, we sliall have, 

272.25 X 160 = 43560 = the square feet in an acre. 

Since there are 9 square feet in a square yard, if the 
last number be divided by 9, we obtain, 

4840 = the number of square yards in an acre. 



PEOBLEM r. 

7. To find the area of a piece of ground in the form 
of a square, rectangle, or parallelogram. 

Multiply the base by the altitude, and the product will express 
the area (Geom., Bk. IV., Prop. IV. and V.) 

1. To find the area of the rectangular 
field ABCD. 

Measure the two sides AB, EG : let us 
suppose that we have found AB = 14 chains 
27 hnks, and BG= 9 chains 75 links. Then, 

AB =14:11 links, 
BC= 975 links. 



ABXB0= 1391325 square links, 
= 13.91325 acres. 
4 



8.65300 roods, 
40 



26.12000 perches. 

Ans. ISA. SB. 26P. 

2. "What is the area of a square field, of which the 
sides are each S3 ch. 81.? 

Ans. lOdA. IE. 29P. 



SEC. 11] 



AREA OP LAND. 



89 



3. What are tlie contents of a rectangular field, of wHcli 
tlie longer side is 49 ch. 27 1., and tlie shorter 38 ch. 71.? 

Ans. 187 A. 2R. IIP. 

4. What are the contents of a fifeld in the form of a 
parallelogram, of which the base is 35 ch. 65 1., and alti- 
tude 61 ch. 4 1. ? 

Ans. 1%1A. 3R 33P. 




PROBLEM IL 

8. To find the contents of a piece of land in the form 
of a triangle. 

FIRST METHOD. 

Measure either side of the triangle 
as BC^ and from the opposite angle 
A let fall a perpendicular AD, and 
measure this perpendicular ; then^ mul- 
tiply the base and perpendicular to- 
gether, and divide the product hy 2, 
the result will express the area of the triangle. Or^ the area 
is equal to the base multiplied by half the perpendicular^ or to 
the perpendicular multiplied hy half the base (Geom., Bk. lY., 
Prop. YL). 

1. YiThat are the contents of a triangle whose base is 
25 ch. 1 1, and perpendicular 18 ch. 14 1. ? 

• Ans. 22 A. 2E. 29P. 

2. What are the contents of a triangle whose base is 

? 
Ans. 7A. IB. 38P. 



SECOND METHOD. 



two sides and their included angle. Then, add 
together the logarithms of the two sides and the logarithmic sine 
of their included angle; from this sum subtract the logarithm 
of the radius, which is 10, and the remainder will he the loga- 
rithm, of double the area of the triangle. Find, from the table, 



90 



ELEMENTS OF SURVEYING. [BOOK II. 



the number answering to this logarithm^ and divide it ly 2 ; the 
quotient will he the required area (Geom. Mens., Prob. II., 
Case 2). 

1, In a triangle ABC, suppose that we have found 
^5=57.65 ck, A (7= 125.81 ch., and the included angle 
CAB=bT 25': required the area. 

Let the required area be designated by 



And 



log 2^- 
Q 



+ log ^^57.65 . 
+ log ^(7 125.81 
^ +log sin A 57° 25' 
loff B . . . 



= 6111.4 



) ; then, 

1.760799 
2.099715 
9.925626 
10 

8.786140. 



= 8055.7 square chains. 

Ans. 805^. 2B. IIP. 



Eemark. In this example, the links are treated as de- 
cimal parts of the chain ; the result, therefore, is in square 
chains and decimal parts of a square chain. 

2. What is the area of a triangle whose sides are 80 
and 40 chains, and their included angle 28° 57' ? 

Ans. 29^. OB. IP. . 



THIRD METHOD. 

Measure the three sides of the triangle. Then, add them 
together and take half their sum. From this half sum subtract 
each side separately. Then, multiply the half sum and the 
three remainders together, and extract the square root of the pro- 
duct : the result will he the area (Geom. Mens., Prob. IL, 
Case 8). 

Or, after having obtained the three remainders, add together 
the logarithm of the half sum and the logarithms of the re- 
spective remainders, and divide their sum by 2 ; the quotient 
will be the logarithm of the area. 

1. Find the area of a triangular piece of ground whose 
sides are 20, 80, and 40 chains. 



SEC. IL] AREA OF LAND. 91 





BY riEST RULE. 




20 


45 45 


45 


80 


-20 -80 


-40 


40 
2)90 
45- 


25 1st rem. 15 2d rem. 
= half sum. Tiien, 


5 3d rem. 



45X25X15X5 = 84375: and -/MSTS = 290.4737 = tlie 
area. 

.. Am. 29A. OB. 8P. 

2. What is the area of a triangle whose sides are 2569, 
4900, and 5035 links? 

BY SECOOT) EULE. 

2569 6252 6252 6252 

4900 -2569 - 4900 - 5035 

5035 3683 1st rem. 1352 2d rem. 1217 3d rem. 



2 )12504 

6252 = half sum. 



Then, 



log 6252 8.796019 

log 3683 8.566202 

log 1352 3.130977 

log 1217 3.085291 



2 )13.578489 
Area in square links, 6155225 . . . 6.789244. 

Ans. 61A. 2B. 8P. 



PEOBLEM IIL 

9. To find the area of a piece of land in the form of 
a trapezoid. 

Measure the two parallel sides, and also the perpendicular 
distance betiveen them. Add the two parallel sides together, 
and take half the sum ; then multiply the half sum hy the 
perpendicular, and the product will he the area (Geom., Bk. 
lY., Prop. Vn.) 



92 ELEMENTS OF SURVEYING. [BOOK II 

1. What is the area of a trapezoid, i \ 

of wliicli tlie parallel sides are 80 and / \ 

49 chains, and the perpendicular distance / \ 

between them 16 ch. 60 l, or 16.60 chains ? '- ^ 



30 + 49 = 79 ; dividing by 2, gives . . 89.5 
multiply by 16.60 



area in square chains 655.700. 

Ans. 65^. IB. IIP. 

2. Eequired the contents, when the parallel sides are 20 
and 82 ch., and the perpendicular distance between them 
26 ch. 

Ans. 67^. 2i?. 16P. 



PROBLEM IV. 

10. To find the area of a piece of land in the form of 
a quadrilateral. 

Measure the four sides of the quadrilateral^ and also one of 
the diagonals: the quadrilateral will thus he divided into two 
triangles, in loth of which all the sides will he known. Then, 
find the areas of the triangles separately, and their sum will he 
the area of the quadrilateral. 

1. Suppose that we have measured J) 

the sides and diagonal AC, of the ^-^^l^ 

quadrilateral ABCD, and found ^^ ! ^ X,^ 

^^=40.05 ch. CZ) = 29.87 ch., ^\. ^\ ?^ 
^(7 = 26.27 ch. ^X) = 37.07 ch., ^^i^ 

and A(7=55ch.: ■« 

required the area of the quadrilateral. 

Ans. 101^. IP. 15P. 

Eemark. Instead of measuring the four sides of the 
quadrilateral, we may let fall the perpendiculars Bh, Dg, on 
the diagonal AC. The area of the triangle may then be 
determined by measuring these perpendiculars and the di- 
agonal AC. The perpendiculars are P^ = 18.95 ch., and 
P6 = 17.92 ch. 



SEC. II.] 



AREA OF LAND; 



93 



PKOBLEM V. 



11. To find tlie contents of a, field having any number 
of sides. 



Measure the sides of the field and also the diagonals: the 
three sides of each of the triangles into which the field will he 
thus divided will then he known, and the areas of the triangles 
may then he calculated hy the preceding rules. Or, measure 
the diagonals, and from the angular points of the field draw 
perpendiculars to the diagonals and measure their lengths: the 
hase and perpendicular of each of the triangles will then he 
known. 

1. Let it be required to determine tbe contents of tbe 
field ABODE, having five sides. 

Let us suppose that we liave mea- 
sured the diagonals and perpendicu- 
lars, and found, 

J. (7=: 36.21 ch., ^(7=89.11 ch., 
J5J = 4.08 ch., Dd=7.2Q ch., 
Aa = 4c.l9 ch. ; required the area of the field. 

Area of triangle ABG= 73.8684 square chains, 
area of " CD^= 141.9698 
area of " ACE= 81.7399 

area of ABODE =297.6776 




Ans. 29A. 8B. IP. 



PROBLEM VI. 

12. To find the contents of a long and irregular figure, 
bounded on one side by a straight line. 

Suppose the ground, of which the contents are required, 
to be of the form ABEeda, bounded on one side by the 
right line AE, and on the other by the curve edca. 

At A and E, the extremities of 
the right hne AE, erect the two per- 
pendiculars Aa, Ee, and on each of 
them measure the breadth of the land. 




94 ELEMENTS OF SURYEYING. [BOOK II. 

Then divide tlie base into any convenient number of equal 
parts, and measure tlie breadth of the land at each point 
of division. 

Add together the intermediate breadths and half the sum of 
the two extreme ones: then multiply this sum hy one of the 
equal parts of the base line^ and the product will he the re- 
quired area very nearly (Mens. Prob. YI.) 

1. The breadths of an irregular figure, at five equidis- 
tant places, being 8.20 ch., 7.40 ch., 9.20 ch., 10.20 ch., and 
8.60 chains, and the whole length 40 chains, required the 
area. 

8.20 4)40 

8.60 10 one of the equal parts. 



2 )16.80 

8.40 mean of the extremes, 35.20 sum, 

7.40 10 

9.20 area 852.00 square ch. 

10.20 
35.20 sum. 

Ans. 35JI. 32P. 

2. The length of an irregular piece of land being 21 ch., 
and the breadths, at six equidistant points, being 4.35 ch., 
5.15 ch., 3.55 ch., 4.12 ch., 5.02 ch., and 6.10 chains: re- 
quired the area. 

Ans. 9^. 2R. SOP. 

3. The length of an irregular piece of land is 80 ch., 
and the breadths at nine equidistant points are 5.75 ch., 
6.12 ch., 4.80 ch., 5.09 ch., 3.87 ch., 5.17 ch., 6.00 ch., 
8.94 ch., and 5.95 ch. : what is the area ? 

Ans. 40J.. SR UP. 

4. The length of an irregular field is 39 rods, and its 
breadths at five equidistant places are 4.8, 5.2, 4.1, 7.3, and 
7.2 rods: what is its area? Ans. 220.35 sq. rods. 

Eemark. If it is not convenient to erect the perpen- 
diculars at equal distances from each other, the areas of 
the trapezoids, into which the whole figure is divided, 
must be computed separately : their sum will be the re- 
quired area. 



SEC. II.] AREA OF LAND. 95 



PROBLEM VII. 




13. To find tlie area of a piece of ground in tlie form 
of a circle. 



Measure the radius AC: then multiply 
the square of the radius hy 8.1416 (Mens., 
Art. 15.). 



1. To find tlie area of a circular piece of land, of wliicli 
tlie diameter is 25 cli. 

Ans. 49^. OR. 14P. 

PROBLEM VIIL 

14. To find tlie contents of a piece of ground in tlie 
form of an ellipse. 

c 

Measure the semi-axes AE, CM Then 
multiply them together, and their jproduct 
ly 3.1416. 

1. To find tlie area of an elliptical piece of ground, of 
wHcli tlie transverse axis is 16.08 cli., and tlie conjugate 
axis 9.72 cli. 

Ans. VIA. \R. 4P. 

Eemark I. Tlie following is tlie manner of tracing an 
ellipse on tlie ground, wlien tlie two axes are known. 

From C, one of the extremities of tlie conjugate axis 
as a centre, and AE lialf tlie transverse axis as a radius, 
describe tlie arc of a circle cutting AE in tlie two points 
F and 0- : these points are called the foci of the ellipse. 

Then, take a tape, the length of which is equal to AB, 
and fasten the two ends, one at the focus F, the other at 
the focus C Place a pin against the tape and move it 
around, keeping the tape tightly stretched: the extremity 
of the pin will trace the curve of the ellipse. 

Remark n. In determining the contents of ground, in 
the examples which have been given, the linear dimensions 
have been taken in chains and decimals of a chain. 




96 ELEMENTS OF SURVETIITG. [BOOK II. 

If the linear dimensions were taken in terms of any 
otlier unit, tHey may be readily reduced to chains. For, 
a chain is equal to 4 rods, equal to 22 yards, equal to 66 
feet. Hence, 

1st. Hods may he reduced to chains and the decimal of a 
chain, hy dividing hy 4. 

2d. Yards may he reduced to chains and the decimal of a 
chain, hy dividing hy 22. 

8d. Feet may he reduced to chains and the decimal of a 
chain, hy dividing hy QQ. 

Eemaek III. If it is tliouglit best to calculate the area, 
witliout reducing the linear dimensions to chains, the re- 
sult can be reduced to acres : 

1st. By dividing it hy 160 when it is in square rods 
(Art. 5). 

2d. By dividing it hy 4840 when it is in square yards 
(Art. 6). 

3d. By dividing it hy 43560 when it is in square feet 
(Art. 6). 



OF LAYING OUT LAND. 

15, The surveyor is often required to lay off a given 
quantity of land, in such a way that its bounding lines 
shall form a particular figure, viz., a square, a rectangle, a 
triangle, &c. He is also often called upon to divide given 
pieces of land into parts containing given areas, or bearing 
certain relations to each other. 

The manner of making such divisions must always de- 
pend on a judicious application of the principles of geom- 
etry to the particular case. 

If, for example, it were required to lay out an acre of 
ground in a square form, it would first be necessary to 
find, by calculation, the side of such a square, and then to 
trace, on the ground, a figure bounded by four equal lines 
at right angles to each other. 



SEC. II.] LAYING OUT LAND. 97 

PEOBLEM I. 

16. To lay out a given quantity of land in a square 
form. 

Reduce the given area to square chains^ or square rods: 
then extract the square root, and the result will he the side of 
the required square. This square being described on the ground, 
will be the figure required. 

1. To trace a square whicli stall contain IbA. OR. 12P. 
First, 15J[ = 60i^=2400P 

Add, 12P ; hence, 

IbA OR 12P=2412P; tlie square root 
of wMcli is 49.11. 

Therefore, if a squ.are be traced on tlie ground, of wliicli 
tlie side is 49.11 rods, it will be tlie required figure. 

2. To trace a square wliicli shall contain 176J.. IR. 24:P. 
First, 176^ = 1760 square chains, 

1R= 2.5 " 
hence, 24P= 1.5 " 

176J- IP 24P= 1764 square chains : the square 
root of which is 42. Hence, if a square be traced on the 
ground, of which the side is 42 ch., it will be the required 
figure. 

PROBLEM XL 

17. To lay out a given quantity of land in a rectangu- 
lar form, having one of the sides of the rectangle given. 

Divide the given area, reduced to square chains or square 
rods, by the given side of the required rectangle, and the quotient 
will be the other side. Then, trace the rectangle on the ground. 

1, To lay off 240 acres in a rectangular form, one of 
the sides being given, and equal to 80 rods. 

First, 240J. = 2400 square chains = 88400 square rods. 

Then, 80)38400(480 rods ; which is the required side 
of the rectangle. 

18. A great number of similar problems might be pro- 
posed. The solution of them does not, however, properly 
belong to surveying. The laying out of the ground, and 



98 ELEMENTS OF SURVEYING. [BOOK II 

the tracing of lines, after tlie figure and area have been 
determined, are the only parts which appertain to a prac- 
tical treatise. The manner of tracing lines having been al- 
ready explained, it seems unnecessary to add the numerous 
examples often given under this head of the subject. 



SECTION III. 



SURVEYING WITH THE COMPASS. — DIVIDING LAND. 

1. Before considering the principles involved in the 
method of surveying now to be explained, it will be ne- 
cessary to describe the instrument principally used in the 
field, and which is called 



THE CIRCUMFERENTER, OR SURVEYOR'S COMPASS. 

PI, 2, Fig. 2. This instrument consists of a compass-box 
DCE^ a magnetic needle, a brass plate AB^ from twelve to 
fourteen inches long, two plain sights, AF and BQ, one 
of which is more fally shown in Fig, 3 ; and a stand, 
which is sometimes a tripod, and sometimes a single staff 
pointed with iron at the lower end, so that it may be 
placed firmly in the ground. 

The open sights, AF and BO^ are placed at right an- 
gles to the plate AB^ and fastened to it firmly by the 
screws a and 5, In each sight there is a large and small 
aperture or slit ; the larger aperture being above the smaller 
in one of the sights, and below it in the other, A hair 
or thread of silk is drawn vertically through the middle 
of the large aperture, as shown in Fig. 8, 

The compass-box DGE is circular, and generally about 
six inches in diameter. At the centre is a small pin, on 
which the magnetic needle is poised. This needle, if al- 
lowed to turn freely around the point of support, will settle 
to a state of rest : the direction which it then indicates, is 
that of the magnetic meridian. 



SEC. Ill] WITH THE COMPASS. 99 

In the interior of tlie compass-box, there is a graduated 
circle divided to degrees, and sometimes to half degrees : 
the degrees are numbered from the extremities of the di- 
ameter NS, both ways to 90°. 

The length of the magnetic needle is a little less than 
the diameter of the graduated circle, so that the needle can 
move freely around its centre, within the circle, and its 
positions be noted on the gi^aduated arc. 

The compass-box is turned about its centre, without 
moving the plate AB, by means of the milled screw L: 
it is fastened to the plate AB, by the screw P. 

In using the compass, it is important to ascertain the 
exact angle which may be included between the magnetic 
meridian and the direction that may be given to the line 
drawn through the eye and the sights AF and BG. 

To effect this, a small arc HI is described on the bar 
AB, having its centre at the centre of the compass-box. 
This arc is divided to degrees, and sometimes to the parts 
of a degree. A vernier is also used, which is permanently 
attached to the compass-box. 

When the point of this vernier coincides with the 
point of the graduated arc HI, the line of the compass-box 
marked NS, lies in the plane of the sights, 

Now, supposing the of the vernier to coincide with 
the of the arc HI, if the end of the needle does not 
stand at one of the lines of division of the gTaduated 
circle, let the whole degrees be read. Then, turn the 
compass-box by means of the screw L, until the needle 
points exactly to the line which marked the whole degrees : 
the space passed over by the of the vernier, shows the 
parts of a degree that are to be added to give the true 
reading. 

SURVEYESTG WITH THE COMPASS. 

2. The line about which the earth revolves is called its 
axis; and the two points in which the axis meets the sur- 
face of the earth, are called the poles. 

3. A plane passed through the axis is called a meridian 



100 ELEMENTS OP SUEVEYING. [BOOK II. 

plane, and its intersection witli tlie surface is called a me- 
ridian line or a meridian. 

4. All tlie meridians converge towards tlie poles, but 
they vary so little from parallelism witliin tlie narrow limits 
of surveys made with, the compass, that they may, without 
error, be regarded as parallel straight lines. 

5. K a magnetic needle be suspended freely and allowed 
to settle to a state of rest, a vertical plane passed through 
its axis is called the plane of the magnetic meridian ; and its 
intersection with the surface of the earth is called the mag- 
netic meridian, or sometimes a North and South line. A 
line perpendicular to a North and South hne is called an 
East and West line. 

6. A line traced or measured on the ground, is called 
a course; and the angle which this hne makes with the 
meridian passing through the -ivr 

point of beginning, is called 
the bearing. 

Thus, if we start from the 
point A, and measure in the 
direction AB. the line AB is 
the course, and the angle JSfAB 
is the bearing. 

When the course, like AB, falls between the north and 
east points, the bearing is read, north 46° east, and is 
written N. 46° E. 

When the course, like AC, falls between the north and 
west points, the bearing is read, north 80° west, and is 
written N. 30° W. 

When the course, like AF, falls between the south and 
east points, the bearing is read, south 70° east, and is writ- 
ten S. 70° E. 

When the course, like AB, falls between the south and 
west points, the bearing is read, south 70° west, and is 
written S. 70° W. 

A course which runs due north, or due south, is desig- 
nated by the letter N or S ; and one which runs due east, 
or due west, by the letter E or W. 




B 



■yT 



E 



\ 



SEC. III.] WITH THE COMPASS. 101 

7. If, after having passed over a course, the bearing is 
taken to the back station, this bearing is called the ha/ik 
sight^ or reverse hearing. 

8. The perpendicular distance between the east and west 
lines drawn through the extremities of a course, is called 
the northing or southing^ according as the course is run to- 
wards the north or south. This distance is also called the 
difference of latitude^ or simply the latitude, because it shows 
the distance which one of the points is north or south of 
the other. 

Thus, in running the course from A 
to B^ AC \& the difference of latitude, c 

north. 

9. The perpendicular distance be- W" 
tween the meridians passing through the 
extremities of a course, is called the de- 
parture of that course, and is east or 
west, according as the course lies on "" 

the east or west side of the meridian passing through the 
point of beginning. 

Thus, in running the course AB, CB is the departure, 
east. 

10. It will be found convenient, in explaining the rules 
for surveying with the compass, to attribute to the lati- 
tudes and departures the algebraic signs, + and — . 

We shall, therefore, consider every northing as affected 
with the sign -f , and every southing as affected with the 
sign — , We shall also consider every easting as affected 
with the sign +, and every westing as affected with the 
sign -. 

11. The meridian distance of a point is its perpendicular 
distance from an assumed meridian. Thus, if the distance 
be estimated from the meridian NS, BG will be the meri- 
dian distance of the point B. 

12. The meridian distance of a line is the meridian dis- 
tance of its middle point, and is east or west, according as 
this point lies on the east or west side of the assumed me- 



102 



ELEMENTS OF SURVEYING. [BOOK II. 



ridian. Thus, FO drawn tliroTigli the middle point of AB, 
is the meridian distance of the line AB. 

The sign + will always be given to the meridian dis- 
tance of a point or line, when it lies on the east of the as- 
sumed meridian, and the sign — , when it lies on the west. 

13. When a piece of ground is to be surveyed, we be- 
gin at some prominent corner of the field, and go entirely 
around the land, measuring the lengths of the bounding 
lines with the chain, and taking their bearings with the 
compass. It is not material whether the ground be kept 
on the right hand or on the left, and all the rules deduced 
for one of the cases, are equally applicable to the other. 
To preserve uniformity, however, in the language of the 
rules, we shall suppose the land to be always kept on the 
right hand of the surveyor. 



FIELD OPERATIONS. 



14. Let ABCD be a piece of 
gTOund to be surveyed, A the point 
where the work is to be begun, 
and NS a meridian. 

On a sheet of paper, rule three 
columns, as follows, and head them 
stations, bearings, distances. 




Stations. 


Bearings. 


Distances. 


1 


N 311° w 


10. 


2 


N" 62f ° E 


9.25 


3 


S 36° E 


7.60 


4 


S 451° W 


10.40 



Place the compass at J., and take the bearing to B, 
which is PAB: suppose this angle has been found to be 
31^°. The bearing from ^ to 5 is then JST. 31^° W. En- 



i 



SEC. Ill] WITH THE COMPASS. 103 

ter tiiis bearing in tlie field notes opposite station 1. 
Then measure the distance from A to B^ which we will 
suppose to be 10 ch., and insert that distance opposite sta- 
tion 1, in the column of distances. 

We next take the bearing from B to 0, N. 62f E., and 
then measure the distance BO— 9 ch. 25 1., both of which 
we insert in the notes opposite station 2. 

At station G we take the bearing to JD, S. 36° E., and 
then measure the distance CD = 7 ch. 60 1., and place them 
in the notes opposite station 3. 

At 1) we take the bearing to A, S. 45^° W., and mea- 
sure the distance DA = 10 ch. 40 1. We shall then have 
made all the measurements on the field which are neces- 
sary to determine the contents of the ground. 

15. Eemark L The reverse bearing or back sight, from 
B to A, is the angle ABH- and since the meridians ISTS 
and HG are parallel, this angle is equal to the bearing 
NAB. The reverse bearing is, therefore, S. 31|-° E. 

The reverse bearing from G, is S. 62f ° W. ; that is, it 
is the angle IGB= QBG. 

And generally, a reverse hearing^ or hack sight, is always 
equal to (he forward hearing^ and differs from it in both of the 
letters by ivhich it is designated. 

16. Eemark II. In taking the bearings with the com- 
pass, there are two sources of error. 1st. The inaccuracy 
of the observations : 2d. Local attractions, or the derange- 
ment which the needle experiences when brought into the 
vicinity of iron-ore beds, or any ferruginous substances. 

To guard against these sources of error, the reverse 
bearing should be taken at every station : if this and the 
forward bearing are of the same value, the work is proba- 
bly right ; but if they differ considerably, they should both 
be taken again. 

17. Remark III. If the forward and back sights at the ' 
end of any course of the survey agree, it may be safely 
assumed, that no local attraction disturbs the needle at 
these points ; and hence, that the next foresight is also free 
from such disturbing causes. The error, therefore, from 



104 



ELEMENTS OF SURVEYING. [BOOK IL 



local attraction, wlien it arises, will first show itself in tlie 
difference between a true foresiglit and an erroneous back 
sight. 

When this difference appears, subtract the back sight 
from the foresight, and call the difference the correction for 
the next foresight. The correction will be positive when 
the foresight is the larger, and negative when it is less. 

Add this correction, with its proper sign, to the fore- 
sight of the next course, when the meridional and longitu- 
dinal letters of that course are both the same, or both dif- 
ferent from the foresight of the previous course, and sub- 
tract it when one of the letters is the same and the other 
different : the result will be the true bearing. The true 
bearing of any other course may be found by the same 
process. 



EXAMPLE. 



True Eoresiglits. 


Back Sights. 


Foresights of next 
Course. 


Foresights 
Corrected. 


1. S 85° 10' W 

2. N 16° 20' E 

3. ]Sri7°25'W 

4. S. 47° 18' E 


N 85° 05' E 
S18°20'W 
S 16° 10' E 

N48°10'W 


S 16° 15' W 
N 15° 25' W 
N 28° 16' E 
S 49° 15' W 


S16°20'W 

N17°25'W 
N 27° 01' E 
N50°07'W 



Note. — If there be no course in the survey in which 
the foreward and back sights agree, take the one in which 
they agree the nearest, and add half the difference of the 
bearings to the least, and treat the result as the true bearing. 

18. Eemark IY. In passing 
over the course AB, the north- 
ing is found to be HB, and the 
departure, which is west, is repre- 
sented by AH. Of the course BG^ 
the northing is expressed by BG, 
and the departure, which is east, 
by GG. Of the course GD, the 
southing is expressed by GI, and 
the departure, which is east, by 
GF. Of the course DA^ the south- 




SEC. Ill] TRAVERSE TABLE. 105 

ing is expressed bj KA, and tlie departure, which is west, 
by DK. It is seen frora the figure, that the sum of 
the northings is equal to HB -\-BG = HG -^ and that the 
sum of the southings is equal to CI-\r KA=PA=^ HG: 
hence, the sum of the northings is equal to the sum of the 



If we consider the departures, it is apparent that the 
sum of the eastings is equal to GC-{- CF= GF] and that 
the sum of the westings is equal to AH+ I)K= GF] hence 
also, the sum of the eastings is equal to the sum of the loestings. 
We therefore conclude, that when any survey is correctly 
made, the sum of the northings will be equal to the sum of the 
southings^ and the sum of the eastings to the sum of the 
westings. 

It would indeed appear plain, even without a rigorous 
demonstration, that after having gone entirely round a 
piece of land, the distance passed over in the direction due 
north, must be equal to that passed over in the direction 
due south ; and the distance passed over in the direction 
due east, equal to that passed over in the direction due 
west. 

Having now explained the necessary operations on the 
field, we shall proceed to show the manner of computing 
the contents of the ground. We shall first explain, 



THE TRAVERSE TABLE AND ITS USES. 

19. This table shows the latitude and departure corres- 
ponding to bearings that are expressed in degrees and 
quarters of a degree from to 90°, and for every course 
from 1 to 100, computed to two places of decimals. 

The following is the method of deducing the formulas 
for computing a traverse table ; by means of these for- 
mulas and a table of natural sines, the latitude and depar- 
ture of a course may be computed to any desirable degree 
of accuracy. 



106 ELEMENTS OF SURVEYING. [BOOK II. 

Let AD represent any course, and ^^ 

NAD = A CB, expressed in degrees and i 
minutes, be its bearing. Let AC he the j / 

unit of measure of the course, and also ^ 

the radius of the table of natural sines X < 

(Bk. L, Sec. IIL, Art. 14). Draw DU and a/-—^ 

CB parallel to NS, and AU perpen- i " 

dicular to AS. Then will DIJ be the ^ 
latitude, and AJE the departure of the course, and CB the co- 
sine, and AB the sine of the bearing. 

From similar triangles we have these proportions, 

AC : CB :: AD : DE, or 

1 : cos of the bearing : : course : latitude, 

AC '. AB :: AD : AU, or 
1 : sin of the bearing : : course : departure. 

Whence, lat. = course X cos of the bearing, 
dep. = course X sin of the bearing. 

We have then the following practical rule for compu- 
ting the latitude and departure of any course. 

Look in a table of natural sines for the cosine and sine of 
the bearing. Multiply each by the length of the course, and the 
first product will be the latitude, and the second will be the 
departure of the given course. 



EXAMPLES. 

1. The bearing is 65° 89', the course 69.41 chains : what 
is the latitude, and what the departure? 

Natural cosine of 65° 89' 41231 

Length of the course 69.41 

Product, which is the Dif. of Latitude, 28.6184871. 

Natural sine of 65° 39' 91104 

Length of the course 69.41 

Product, which is the Departure . . 63.2352864. 



SEC. Ill] TRAVERSE TABLE. 107 

2. The bearing is 75° 47', tlie course 89.75 chains : what 
is the latitude, and what the departure? 

Natural cosine of 75° 47' . 24559 

Length of course 89.75 



Product, which is the Dif. of Latitude, 22.0417025. 

Natural sine of 75° 47' 96937 

Length of course 89.75 

Product, which is the Departure . . 87.0009575. 

20. In this manner the traverse table given at the end 
of the book has been computed. When the bearing is 
given in degrees aiid quarters of a degree, and the differ- 
ence of latitude and departure are required to only two 
places of decimals, they may be taken directly from the 
traverse table. 

If the bearing is less than 45°, the angle will be found 
at the top of the page ; if greater, at the bottom. Then, 
if the distance is less than 50, it will be found in the col- 
umn " distance," on the left hand page ; if greater than 50, 
in the corresponding column of the right hand page. 

The latitudes or departures of courses IN 

of different lengths, but which have the ^ 

same bearing, are proportional to the 
lengths of the courses. Thus, in the " 
figure, the latitudes AG, AO, or the de- 
partures GF, CB, are to each other as 
the courses AF, AB. S 

Therefore, when the distance is greater than 100, it 
may be divided by any number which will give an exact 
quotient, less than 100 : then the latitude and departure of 
the quotient being found and multiplied by the divisor, the 
products will be the latitude and departure of the whole 
course. It is also plain, that the latitude or departure of two 
or more courses, having the same bearing, is equal to the 
sum of the latitudes or departures of the courses taken sepa- 
rately. 

Hence, if we have any number greater than 100, as 
614, we have only to recollect that, 610 -f 4 = 614 ; and 
also, that the latitude and departure of 610, are ten times 



n / 



E 



108 ELEMENTS OF SURVEYIITG. [BOOK II. 

as great, respectively, as tlie latitude and departure of 
61 : tliat is, equal to the latitude and departure of 61 mul- 
tiplied by 10, or with, the decimal point removed one place 
to the right. 

EXAMPLES. 

1. To find the latitude and departure for the bearing 



Latitude' for 610 . . 530.90 
Latitude for 4 . . 8.48 



Latitude for 614 . . 534.38 



Departure for 610 . . 300.40 
Departure for 4 . . 1.97 

Departure for 614 . . 302.37 

In this example, the latitude and departure answering 
to the bearing 29|°, and to the distance 61, are first taken 
from the table, and the decimal point removed one place 
to the right : this gives the latitude and departure for the 
distance 610 ; the latitude and departure answering to the 
same bearing and the distance 4, are then taken from the 
table and added. 

2. To find the latitude and departure for the bearing 
62^°, and the course 7855 chains. 

Latitude for 7800 . 3602.00 Departure for 7800 . 6919.00 
Latitude for 55 . 25.40 Departure for 55 . 48.79 

Departure for 7855 . 6967.79 



Latitude for 7855 . 3627.40 



Eemaek. When the distances are expressed in whole 
numbers and decimals, the manner of finding the latitudes 
and departures is still the same, except in pointing off the 
places for decimals : but this is not difficult, when it is re- 
membered that the column of distances in the table, may 
be regarded as decimals, by removing the decimal point to 
the left in the other columns. 

3. To find the latitude and departure for the bearing 
47f °, and the course 37.57. 



Latitude for 37.00 . 24.88 
Latitude for .57 . .38 



Latitude for 37.57 . 25.26 



Departure for 37.00 . 27.39 
Departure for .57 . .42 

Departure for 37.57 . 27.81 



SEC. Ill] OF BALANCING. 109 



OF BALANCING THE WORK. 

21. The use of tlie traverse table being explained, we 
can proceed to compute tlie area of tlie ground. 

The field notes having been completed, rule a new table, 
as below, with four additional columns, two for latitude, 
and two for departure. 

Then find, from the traverse table, the latitude and de- 
parture of each course, and enter them in the proper col- 
umns opposite the station. 

Then add up the column of northings, and also the col- 
umn of southings : the two sums should be equal to each 
other. If they are not, subtract the less from the greater ; 
the remainder is called the error in latitude. This error 
takes the name of that column which is the less. For 
example, if the sum of the northings is less than the sum 
of the southings, the error is called, error in northing : but 
if the sum of the southings is less than the sum of the 
northings, the error is called, error in southing. We find 
the error for each particular course by the following pro- 
portion. 

As the sum of the courses 
Is to the error of latitude, 
So is each particular course 
To its correction. 

The error thus found may be entered in a separate col- 
umn ; after which add it to the latitude of the course when 
the error and latitude are of the same name, but subtract 
it when they are of different names. This will make the 
sum of the northings equal to the sum of the southings, 
and is called balancing the work. The northings and south- 
ings thus corrected are entered in columns on the right, 
under the head balanced. 

The eastings and westings are balanced in the same 
manner ; the difference between their sums being called 
error in departure. 

For an example, we will resume the one already con- 
sidered. 



no 



ELEMENTS OF SURVEYING. [BOOK IL 



Sta. 


Bearings. 


Distan- 
ces. 


LATITUDE. 


DEPARTURE. 


Cor. 
Lat. 


Cor. 
Dep. 


BALANCED. | 


N. 
+ 


S. 


E. 
+ 


W. 


N. 
+ 


S. 


E. 

+ 


W. 


1 

2 
3 

4 


N 31io W 
N 62JO K 
S 360 E 

S 45iO W 


10. 
9.25 
7.60 

10.40 


8.53 
4.23 


6.15 

7.29 


8.22 
4.47 


5.22 
7.4i 


+ 0.18 
+ 0.17 
— 0.14 
-0.19 


+ 0.02 
-0.01 
— 0.01 
+ 0.02 


8.71 
4.40 


6.01 
7.10 


8.21 
4.46 


5.24 
7.43 


Sum of courses, 37.25 


12.76 


13 44 
12.76 


1269 
12.63 


12.63 


13.11 


13.11 


12.67 


12.67 


Error in Northing . 


. . 


0.68 


0.06 


Error 


in Westing. 











As 37.25 : 0.68 

As 37.25 : 0.68 

As 37.25 : 0.68 

As 37.25 : 0.68 

As 37.25 : 0.06 
As 37.25 : 0.06 
As 37.25 : 0.06 
As 37.25 : 0.06 



10 : 0.18 error in lat. of 1st course. 

9.25 : 0.17 error in lat. of 2d course. 

7.60 : 0.14* error in lat. of 3d course. 

10.40 : 0.19 error in lat. of 4tli course. 

10 : 0.02* error in dep. of 1st course. 

9.25 : 0.01 error in dep. of 2d course, 

7.60 : 0.01 error in dep. of 3d course. 

10.40 : 0.02 error in dep. of 4tli course. 



22. Remark I. In finding tlie error in latitude or de- 
parture, for a particular course, the last figure is sometimes 
doubtful : in which case it is best to mark it, as in the 
third proportion for error in latitude, and the first for er- 
ror in departure ; and then, if the figures taken do not 
balance the work, let each be increased or diminished by 1. 

23. Eemark II. It has already been observed (Art. 18), 
that if the measurements on the field be correctly made, 
the sums of the northings and southings will be equal to 
each other, as also those of the eastings and westings. It 
is the opinion of some surveyors, that when the error in 
latitude or departure exceeds one link for every five chains 
of the courses, the field notes ought not to be relied on. 
This, perhaps, is a higher degree of accuracy than can be 
attained. The error, however, should always be made 
considerably less than one link to a chain. 

24. The following is an example in which the latitude 
and departure of each course have been computed from 
the table of natural sines. 



SEC. Ill] 



OF BALANCING. 



Ill 



— 


Bearing.. 


Dut. 


Dif. ofLatitnde. 


Departure. 


Balanced. ] 


N. 


S. 


E. 


W. 


N. 


S. 


E. 


W. 


/ 
N 45 65 W 


63 ch. 


36.81210 






■ 
38.01149 


36.65903 






38.01149 


2 


N 4 50K 


14.40 


14.13513 




6.26894 




13.12813 




6.26894 




3 


N 89 05 E 


125.60 


2.00800 




125.48368 




1.96126 




126.49228 




4 


S 160W 


11.80 




11.16338 




2.29688 




12.11110 




2.29688 


5 


S 7 40E 


31.20 




30.92101 


4.16239 






31.12138 


4.16239 




6 


N 89 25 W 


36.50 


0.36139 






35.49822 


0.36139 






35.49822 


1 


S 84 35 W 


40. 




3.11600 




39.82120 




3.80352 




39.81260 


8 


S 14 35 W 


21. 




5.58264 




20.24442 




5.61385 




20.24442 








113.31662 
112.04309 


112.04309 


136.91501 


135.93221 
135.91601 


112.10986 


112.10985 


136.92361 


136.92361 



Instead of balancing by the metbod jnst explained, we 
divide eacb error by two. Now if we subtract half the 
error in southing from the column of northings, and at the 
same time add it to the column of southings, these two 
columns will exactly balance. In like manner, if we sub- 
tract half the error in easting from the column of westings, 
and at the same time add it to the column of eastings, 
these columns will also balance. 

The errors should be distributed in proportion to the 
lengths of the courses, but this may be done with sufficient 
accuracy without making the proportions. If any of the 
courses have been run over rough ground, the probability 
is that the errors belong to these courses, and they should 
be distributed among them. 

In this example we separate the half error in southing 
into the three parts .40700, .21302, and .04674, and subtract 
them respectively from the northings of courses 2, 1, and 
3, and then place the northings in the balanced columns. 
For the southings we separate the half error into the four 
parts .40772, .20031, .03121, and .02752, and add them respec- 
tively to the southings of the courses '4, 5, 8, and 7. We 
then enter the southings in the balanced columns. As the 
error in easting is so small, we add half of it to the east- 
ing of course 3, and subtract half from the westing of 
course 7. 



112 ELEMENTS OF SURVEYING. [BOOK IL 

OF THE DOUBLE MEEIDIAN DISTANCES OF THE COUESES. 

25. After tlie work lias been balanced, tlie next thing 
to be done is to calculate the double meridian distance of 
each course. 

For this purpose, a meridian line is assumed, lying 
either wholly without the land, or passing through any 
point within it. It is, however, most convenient to take 
that meridian which passes through the most easterly or 
westerly station of the survey ; and these two stations are 
readily determined by inspecting the field notes. 

Having chosen the meridian, let the station through 
which it passes, be called tYiQ ^ principal station, and the 
course which begins at this point, the first course. Care, 
however, must he taken, not to confound this with the course 
which legins at station 1, and which is the first course that is 
entered in the field notes. 

It has already been remarked (Art. 10), that all de- 
partures in the direction east, are considered as plv:S, and 
all departures in the direction west as minus. 

26. To deduce a rule for finding the double meridian 
distances of the courses. Let BO n 

represent any course, and AB the 

preceding Course ; also, let JD and j^ 

E be their middle points. Draw iXj: 

EH, CM, and DG, perpendicular to i |\. 

the assumed meridian NS. Draw | j i X^ 

also AI, EK, and BL, parallel to a\ -j:— -^~£|-\i5 

NS. Then 2DG is the double me- | L_\ 

ridian distance of the course BC, 
and 2EH= IKO, is the double me- ^ 
ridian distance of the course AB. 

Now, 2DG = 2GK+2KL + 2LD; but 2KL = IL is the 
departure of the course AB, and 2LD = MG is the depar- 
ture of the course BC ; 

consequently, 2GB = 2 GK+ IL + MC; 

hence, the double meridian distance of a course, is equal 
to the double meridian distance of the preceding course 



SEC. Ill] DOUBLE MERIDIAN DISTANCES. 113 

plus the departure of tliat course plus tlie departure of the 
course itself; if there is no preceding course, the first 
two terms become zero. We therefore have the following 



RULE. 

I. The double meridian distance of the first course is equal 
to its departure. 

II. The double meridian distance of the second course is 
equal to the double meridian distance of the first course^ plus 
its departure, plus the departure of the second course. 

III. The double meridian distance of any course is equal 
to the double meridian distance of the preceding course, plu^ 
its departure, plus the departure of the course itself 

27. Eemark. It should be recollected that plus is here 
used in its algebraic sense, and that when the double me- 
ridian distance of a course and the departure which is to 
be added to it, are of different names, that is, one east and 
the other west, they will have contrary algebraic signs ; 
hence, their algebraic sum will be expressed by their dif- 
ference, with the sign of the greater prefixed to it. 

If the assumed meridian cuts the enclosure, the double 
meridian distances, estimated to the lefb, must be taken 
with the minus sign. 

The double meridian distance of the last course should 
be equal to the departure of that course. A verification 
of the work is, therefore, obtained by comparing this double 
meridian distance with the departure of the course. 

28. To apply the above rule to the particular example 
already considered (Art. 21), rule a new table as below, in 
which are entered the balanced northings and southings, and 
the balanced eastings and westings. 

In this table there is but a single column for the dif- 
ferences of latitude, and a single column for the departures. 
The + sign shows when the difference of latitude is north, 
and the — sign when it is south. The + sign also shows 
when the departure is east, and the — sign when it is west. 
8 



114 



ELEMENTS OF SURVEYING. [BOOK II. 



Sta. 


Bearings. 


Distances. 


Dif. Lat. 


Dep. 


D. M. D. 


1 

2^ 

3 

4 


N 81i° W 
N 62f ° B 
S 86° E 

s 451-° W 


10. 
9.25 

7.60 
10.40 


+ 8.71 

+ 4.40 
-6.01 
-7.10 


-5.24 
+ 8.21 
+ 4.46 
-7.43 


+ 17.91 

- 7.43 

- 5.24 


+ 5.24 
8.21 

+ 8.21 
+ 8.21 
+ 4.46 


+ 20.88 
+20.88 

+ 4.46 
- 7.43 


+ 17.91 



We see, from inspecting the notes, tliat 2 is the most 
"westerly, and 4 the most easterly station. Either of them 
may, therefore, be taken for the principal station. Let us 
assume 2 for the principal station, and distinguish it by a 
star, thus *. 

Having done so, we enter the departure 8.21 in the 
column of double meridian distances, which gives the 
double meridian distance of the first course. The double 
meridian distances of the other courses are calculated ac- 
cording to the rule ; and as the last, opposite to station 1, 
is equal to the departure of the course, the work is known 
to be right. 

29. Having shown the manner of computing the double 
meridian distance of each course, we shall now deduce a 
rule for finding the 

AEEA. 



Let us still consider the same 
example. We will first write the 
differences of latitude and the 
double meridian distances of the 
courses, in the following table. 




SEC. Ill] 



THE AREA. 



115 



Stations. 


Dif. of Latitude. 


D. M. D. 


Area. 
+ 


Area. 


1 


+ cB 


+ 2ha 


2cAB 




2* 


+ Bs 


+ 2qp 


2BsG 




3 


-yD 


+ 2nh 




2ms GD 


4 


-Df 


+ 2ed 




2cmDA 



It is evident, tliat cB multiplied by 2ha = cA^ will give 
double the area of the triangle cAB. But cB and la are 
both plus ; hence, the product will be plus, and must be 
put in the column of plus areas. Double the area of 
the triangle BsG^ is equal to Bs multiplied by 22'p, which 
product is also plus. 

The area of the trapezoid msGD is equal to yD = ms 
multiplied by nh (Geom., Bk. lY., Prop. YII., S.) ; hence, 
double the area is equal to yD into 2nh. But since yD is 
minus, and 2nh plus, it follows that the product will be 
negative ; hence, it must be placed in the column of nega- 
tive areas. 

Double the area of the trapezoid cADm, is equal to 
Df-=mc multiplied by 2de: but, since Df is negative and 
2de positive, the product will be negative. 

It is now evident that the difference between the two 
columns is equal to twice the contents of the figure ABGD : 
and since the same may be shown for any other figure, we 
may write, for finding the areas, the following general 



RULE. 

I. Multiply the double meridian distance of each course by 
its northing or southing, observing that like signs in the multi- 
plicand and multiplier give plus in the product^ and that un- 
like signs give minus in the product. 

II. Place all the products which have a plus sign, in one 
column, and all the products which have a minus sign, in an- 
other. 

III. Add up the columns separately and take their difference : 
this difference will be double the area of the land. 



116 



ELEMENTS OF SURVEYIIfG. [BOOK 11. 



SO. We will now make tlie calculations in numbers. 
Having balanced tbe work, we can place it in tbe follow- 
ing table. 



Sta. 


Beanngs. 


rsst. 


Dif. Lat. 


Dep. 


D. M. D. 


Ares. 

+ 


Area. 


1 


N 31iO W 


10. 


+ 8.71 


-554 


+ 5.24 


45.6404 




2* 


N62JOE 


9.25 


+ 4.40 


+ 8.21 


+ 8.21 


36.1240 




3 


S 36° E 


7.60 


-6.01 


+ 4.46 


+ 20.88 




125.4888 


4 


S45iOW 


10.40 


-7.10 


-7.43 


+ 17.91 




127.1610 














81.7644 


252.6498 
81.7644 



Area in square chains 
Dividing by 10 . , . 



Am. BjI. 2R. 7P. 



22170.8854 
85.4427 
8.54427 

4 

2.17708 

40 

r . 7.08320 



Observing in tbe field notes that station 2 is the most 
westerly point of the land, we assume the meridian wMcb 
passes through this point, as the one from which the me- 
ridian distances are to be calculated. We mark the prin- 
cipal station with a star. 

Opposite station 2, we enter, in the column of double 
meridian distances, headed D. M. D., the departure of the 
course from 2 to 3, which is the double meridian distance 
of that course, and plus. To this we add the departure 
of the course, and also the departure of the next course : 
their sum is the double meridian distance of the course 
from 3 to 4. 

To the last sum add the departure opposite station 3, 
and the minus departure opposite station 4 : their algebraic 
sum is the double meridian distance from 4 to 1. 

To the last sum add the last departure, which is minus, 
also the next departure which is likewise minus : this will 
give the double meridian distance of the course from 1 to 
2, which is equal to its departure. 

Then forming the products, adding them together, ta- 
king their difference, and dividing it by 2, according to 
the rule, we obtain the contents of the ground. 



SEC. Ill] 



OF PLOTTING. 
OF PLOTTING. 



117 



81. It only remains to make 
a plot of the ground. 

For this purpose, draw any 
line, as NS, to represent the me- 
ridian passing through the princi- 
pal station ; and on this line take 
any point, as B, to represent that 
station. 




FIRST METHOD. 

Having fixed upon the scale on which the plot is to be 
made, lay off from B on the meridian, a distance Bs equal 
to the difference of latitude of the first course, and at s 
erect a perpendicular to the meridian, and make it equal 
to the departure of the first course : then draw BO^ which 
will be the first course. 

Through G draw a meridian, and make Cf equal to the 
difference of latitude of the second course, and through / 
draw a perpendicular /D, and make it equal to the depar- 
ture of the second course : draw GD, and it will be the 
second course. 

Lay down, in the same manner, the courses DA and 
ABj and the entire plot will be completed. 



SECOND METHOD, 

The work may be plotted in another manner, thus. 
At the principal station B^ lay off an angle equal to the 
bearing from B to (7, which will give the direction of BG. 
Then, from the scale of equal parts, make BG equal to the 
first course, this will give the station G. 

Through G draw a meridian, and lay off an angle equal 
to the bearing from G to i), and then lay off the course 
GD. Do the same for the bearing at D and the course 
DA ; also, for the bearing at A and the course AB^ and a 



11! 



ELEMENTS OF SURVEYING. [BOOK 11. 



complete plot of tlie ground will thus be obtained. If the 
work is all right, the last line AB will exactly close the 
figure. This plot is made on a scale of 10 chains to an inch. 
1. It is required to determine the contents and plot of a 
piece of land, of which the following are the field notes, viz. 



Stations. 


Bearings. 


Distances, 


1 


N 461° W 


20 ch. 


2 


N 51|° E 


13.80 


8 


E 


21.25 


4 


S56°E 


27.60 


5 


S 33i° W 


18.80 


6 


N74i° W 


80.95 



CALCULATIOlSr. 



Sta- 

tiODB. 


Bearings. 


Dis. 


Dif. Lat. 


Dep. 


BALANCED. 


D.M.D. 
+ 


AREA. 

+ 


AREA. 


N 
+ 


S 


E 

+ 


W 


Lat. 


Dep. 


1 


N 46iO W 


20 ch 


13.T7 






14.51 


+13.88 


-14.56 


14.56 


202.0928 




2* 


N 51J0 E 


13.80 


8.54 




10.84 




+8.61 


+10.81 


10.81 


93.0741 




3 


E 


21.25 






21.25 






+21.20 


42.82 






4 


S 5G0 E 


27.60 




15.44 


22.88 




—15.29 


+22.82 


86.84 




1327.7836 


5 


S 33iO W 


18.80 




15.72 




10.31 


-15.63 


-10.36 


99.30 




1552.0590 


6 


N 74iO W 


30.95 


8.27 






29.83 


+8.43 


-29.91 


59.03 


497.6229 




Sum of courses r32.4U 


30.58 


31.16 
30.58 


54.97 
54.65 


54.65 




792.7898 2879.8426 
792.7898 




Erro 


innoi 


thing . 


. 0.58 


0.32 


Er 


or in We 


sting 




2 


)2087.0528 



Jlns. 104.4 liJ 16P 1043.5264 



Plot of the example. 




SEO. III.] 



PROBLEMS. 



119 



82. Eemakk. "When a bearing is due east or west, the 
error in latitude is nothing; the course must then be sub- 
tracted from the sum of the courses, and the remainder 
taken in balancing the columns of latitude. In the last 
example, the 3d bearing is due east, and the first term of 
the several proportions for error in latitude, was 132.40 — 
21.25 = 111.15. 

In like manner, if a bearing is due north or south, the 
error in departure is nothing ; and the sum of the courses 
must be diminished by this course, before balancing the 
columns of departure. 

2. Eequired the contents, and plot of a piece of land, 
of which the following are the field notes. 



Stations. 


Bearings. 


Distances. 


1 


S 34° W 


3.95 ch. 


2 


S 


4.60 


3 


S 36i° E 


8.14 


4 


N 59i° E 


3.72 


5 


N25° E 


6.24 


6 


]sri6° w 


3.60 


7 


N65° W 


8.20 



Am. lOA. OB. bP. 



3. Eequired the contents and plot of a piece of land, 
from the following field notes. 



Stations. 


Bearings. 


Distances. 


1 


S 40° W 


70 rods 


2 


N45° W 


89 


3 


N36° E 


125 


4 


N 


54 


5 


S 81° B 


186 


6 


S 8°W 


137' 


7 


W 


130 



Am. 201 A. SB. 33P. 



120 



ELEMENTS OF SURVETIN-G. [BOOK 11. 



4. Eequired tlie contents and plot of a piece of land, 
from the following field notes. 



stations. 


Bearings. 


Distances. 


1 


S 40i° E 


81.80 ck 


2 


N54° E 


2.08 


3 


N 29i° E 


2.21 


4 


N 28f ° E 


85.35 


5 


N57° W 


21.10 


6 


S 47° W 


81.80 



Ans. 92A. SB. 32P. 

5. Eequired tlie area of a survey of wHcli the follow- 
ing are the field notes. 



Stations. 


Bearings. 


Distances. 


1 


N 42° E 


5.00 ch. 


2 


East. 


4.00 


8 


N 9° E 


4.00 


4 


S 69° E 


5.56 


5 


S 86° E 


7.00 


6 


S 42° W 


4.00 


7 


S 75° W 


10.00 


8 


N 39° W 


7.50 



If, in this example, we assume 1 as the principal sta- 
tion, the double meridian distances will all be plus, and 
the positive area will exceed the negative. 

In balancing we shall find the error in southing to be 
.28 ch. and in westing .22 ch. The area is 13^. OR IIP. 
It should however be remarked, that in all the examples 
the answers may be slightly varied by distributing the 
corrections. 

6. What is the area of a survey of which the following 
are the field notes. 



SEC. Ill] 



PROBLEMS. 



121 



Stations. 


Bearings. 


Distances. 


1 


N 75° 00' E 


54.8 rods. 


2 


N 20° 30' B 


41.2 


3 


East. 


64.8 


4 


S 83° 30' W 


141.2 


. 5 


S 76° 00' W 


64.0 


6 


Nortli. 


36.0 


7 


S 84° 00' W 


46.4 


8 


N 63° 15' W 


46.4 


9 


N 36° 45' E 


76.8 


10 


N 22° 30' E 


56.0 


11 


S 76° 45' E 


48.0 


12 


S 15° 00' W 


43.4 


13 


S 16° 45' W 


40.5 

1 



In this survey 4 is the most easterly and 9 the most 
westerly station. The area is equal to 110^. 2B. 23P. 
It may vary a little, on account of the way in which the 
balancing is done. 

7. What are the contents of a piece of land of which 
the following are the field notes? 



stations. 


Bearings. 


Distances. 


1 


S 75° W 


13.70 ch. 


2 


S 20i° W 


10.30 


3 


West. 


16.20 


4 


N 33i° E 


35.30 


5 


N76° E 


16.00 


6 


South. 


9.00 


7 


]Sr84° E 


11.60 


8 


S 531° E 


11.60 


9 


S 36f ° W 


19.20 


10 


S 22i° W 


14.00 


11 


N 76f ° W 


12.00 


12 


N15° E 


10.85 


13 


N 161° E 


10.12 



122 



ELEMENTS OF SURVEYING. [BOOK IL 



In this survey 4 is tlie most westerly station and 9 tlie 
most easterly. The area is llOA. 2R. 23P. The result 
may, however, as in the other examples, be slightly varied 
by the balancing. 

8. What is the area of a survey of which the following 
are the notes? 



stations. 


Bearings. 


Distances. 


1 


S 46^ E 


80 rods 


2 


S 5ir w 


55.20 


3 


West. 


85 


4 


N66° W 


110.40 


6 


N 33i° E 


75.20 


6 


S 74^° E 


123.80 



Arts 104^. \R. 16P. 



I. To determine the contents and houndary of a piece of land, 
hy means of offsets from the principal lines. 

83. An offset is a line measured perpendicular to a 
course, and may lie either on the right or left of it. 

Let ABCDE be a piece of 
ground to be surveyed. Let us 
suppose it to be bounded on the 
west and north by a fence and 
road, and on the east and south 
by a creek or river. 

Assume as stations the prin- 
cipal points J., Bj G, D, and E. 
Take, with the compass, the bear- 
ings from A to B, from B to C^ 
from G to Z), from D to E, and 
from Eio A', and measure the dis- 
tances AB, BG, GD, BE, and EA. 

At convenient points of the course AB, as a, c, and f 
measure the offsets oh, cd, fg. Then, having measured 
these lines, as also the distances Aa, ac, cf, and fB, enough 




REO. Ill] 



PROBLEMS. 



123 



will be known to determine tlie area wMcli lies without tlie 
station line AB. The points 5, d and ^, of the fence which 
runs from A to B^ are also determined. 

Erect, in a similar manner, offsets to the other courses, 
and determine the areas which lie without the station lines. 
These several areas being added to the area within the 
station lines, will give the entire area of the ground. 

If the offsets fall within the station lines, the corres- 
ponding area must be subtracted from the area which is 
bounded by the station lines. 



II. To determine the hearing and distance from one point to 
another, when the points are so situated that one cannot he 
seen from the other. 

34. Let A and G be the two 
points, and AB a meridian pass- 
ing through one. of them. From 
either of them, as A^ measure a 
course J.2, of a convenient length 
in the direction towards C, and 
take the bearing with the com- 
pass. At 2, take the bearing of 
a second course, and measure the 
distance to 3. At 3, take a third 
bearing and measure to 4. At 
4, take the bearing to (7, and 
measure the distance from 4 to C. 




Then, the difference between the sum of the northings 
and the sum of the southings wiU be represented by AB, 
and the difference between the sum of the eastings and 
the sum of the westings by BO. The base AB, and the 
perpendicular BC of the right-angled triangle ABG, are then 
known. The angle at the base, BAG, is the bearing from 
J. to O ; or the equal alternate angle at G is the bearing 
from G to A, and the hypothenuse AG ib the distance. 

35. Having measured the bearings and courses on the 
field, form a table, and find the base and perpendicular 
of the right-angled triangle, in numbers. 



124 



ELEMENTS OF SURVEYING. [BOOK II. 



Stations. 


Bearings. 


Distances. 


N. 


s. 


E. 


w. 


1 


Ner w 


40cli 


19.39 






34.98 


2 


N42°W 


41. 


30.47 






27.43 


3 


N12°E 


16.10 


15.75 




3.35 




4 


N47°E 


32.50 


22.16 




23.77 








AB 


= 87.77 




27.12 


62.41 



27.12 



(7j5= 35.29 ch. 



Eemark. Had any of the 
courses run south, AB would have / 
been equal to the sum of the ^X 
northings, minus the sum of the J 
southings. 3I 


\ " 


To find the angle BAG, or the \ 


\ 


bearing from A to C. 

As radius : tan ^ : : AB : BO, 
or AB : BC :: B : tan A : 

that is. 


^\^ Vi- 
A 


As AB 87.77 . ar. comp. 

: BO 35.29 

: : B 


8.056654 
1.547652 
10. 


: tan A 21° 54' 12" 


9.604306 


To find the distance AC. 




As sin A 21° 54' 12" ar. comp. 

: B 

: : BO 35.29 . , . . 


0.428242 
10. 
1.547652 


: ^C94.6 .... 


1.975894 



Hence, the bearing and distance are both found. 



OF SUPPLYING OMISSIONS IN THE FIELD NOTES. 

36. The last problem affords an easy method of finding 
the bearing and length of one of the courses of a survey, 



SEC. Ill] 



PROBLEMS. 



125 



wlien tlie bearings and lengths of all the others are known. 
It may be necessary to use this method when there are 
obstacles which prevent the measuring of a course, or when 
the bearing cannot be taken. Indeed, two omissions may 
in general be supplied by calculation. It is far better, 
however, if possible, to take all the notes on the field. 
For, when any of them are supplied by calculation, there 
are no tests by which the accuracy of the work can be as- 
certained, and all the errors of the notes affect also the 
parts which are supplied. 



1. In a survey we have the following notes 



stations. 


Bearings. 


Distances. 


1 
2 

3 

4 


N 31i° W 
N 62f ° E 

Lost. 
S 45i° W 


10 ch. 
9.25 

Lost. 
10.40 



What is the bearing and distance from station 3 to 4 ? 

^^ ( Bearing, S 38° 62' E. 
^* 1 Distance, 7.03 ch. 

2. In a survey we have the following notes: 



stations. 


Bearings. 


Distances. 


1 


S 401" B 


31.80 ch. 


2 


N54° B 


2.08 


3 


Lost. 


Lost. 


4 


N 281° E 


35.35 


5 


N57° W 


21.10 


6 


S 47° W 


31.30 



What is the bearing and distance jfrom 3 to 4? 

^^ (Bearing, N 34° 47' E. 
' I Distance, 2.19 ch. 



126 



ELEMENTS OF SURVEYING. [BOOK II. 



III. To determine the angle included between any two courses^ 
when their bearings are known. 



87. Let NS be a meridian 
passing through A. 

Let AB, AC, AH, AD, and 
AF, be five courses running 
from A. We readily deduce 
the following 




PRINCIPLES. 



^(7 is N 26^ 
AH is N 65^ 






(7^5^=39° 



AB is N 46° E 
AG is N 26° W 



CAB = 12' 



When the meridional letters 
are alike, and those of depar- 
ture also alike, the difference of 
the hearings is the angle between 
the courses. 

When the meridional letters 
are alike, and those of depar- 
ture unlike, the sum of the bear- 
ings is the angle between the 



AGi& N 26° W 

AD is s m" w 
C4i> = 180°-92°=88° 



AC is N 26° W 
AF is S m° E 



CAi^=180°-40°=140° 



When the meridional letters 
are unlike, and those of depar- 
ture alike, the angle betiveen the 
courses is equal to 180°, minus 
the sum of the bearings. 

When the meridional letters 
are unlike, and those of depar- 
ture also unlike, the angle be- 
tween the courses is equal to the 
difference of the bearings taken 
from 180°. 



Eemark. The above principles are determined, under the 
supposition that the two courses are both run from the 
angular point. Hence, if it be required to apply them to 



SEC. Ill] OF DIVIDING LAND. 127 

two courses run in tlie ordinary way, as we go around the 
field, tlie bearing of one of tliem must be reversed before 
the calculation for the angle is made. 

1. The bearings of two courses, from the same point, 
are N 37° E, and S 85° W : what is the angle included 
between them? 

Ans. 132°. 

2. The bearings of two adjacent courses, in going round 
a piece of land, are N 39° W, and S 48° W : what is the 
angle included between them? 

Ans. 87°. 

3. The bearings of two adjacent courses, in going round 
a piece of land, are S 85° W, and N 69° W : what is the 
angle included between them? 

Ans. 154°. 

4. The bearings of two adjacent courses, in going round 
a piece of land, are N 55° 30' E, and S 69° 20' E : what 
is the angle included between them? 

Ans. 124° 50'. 

OF DIVIDING LAND. 

38. Fields are so variously shaped that it is difficult 
to give rules that will apply to all cases. It is by practice 
alone that facility is obtained in that branch of survey- 
ing relating to the division of estates. We shall add only 
a few examples that may serve as general guides in the 
application of the principles of Plane Geometry to such 
cases as may arise. 

I. To run a line from the vertex of a triangular field which 
shall divide it into two parts, having to each other the 
ratio of M to N. 

39. Let ABG be any triangular field. 
Divide the side BC into two 

parts, such that (Geom., Bk. IV., 
Prob. 1.) 

BD I DC '.: m : w, ^ 

and draw the line AD: B D 

then will, ABD : DAG : : m : n. 





128 ELEMENTS OF SURVEYING. [BOOK II. 

For, tlie two triangles ABD^ ADG having tlie same alti- 
tude are to each other as their bases (Geom., Bk. IV., P. 6, 
C): hence, the triangle is divided into parts having the 
ratio of m to n. 

II. To run a line parallel to one side of a triangular field, 
that shall form with the parts of the two other sides a 
triangle equivalent to the — part of the field. 

40. Let OBA represent a triangular field and CA the 
side parallel to which the dividing line is to be drawn. 



On the side BC describe 
a semicircle : then divide BC 
at JD, so that 

BD '. BC '.: m : n. 



At D, erect the perpendicular BG to the diameter BO, 
and draw BG. Then, with ^ as a centre, and BG as a 
radius, describe the arc of a circle cutting BC at M 
Through E draw UF parallel to CA, and it will divide the 
triangle in the required ratio. 

For, (Geom., Bk. IV., P. 23.) 

BG^=BE' = BCxBD: 

„ o BD 

or, BE^ = BC''X jg^', whence, 

be"" '. BG" \: BD '. BC :: m : n. 

But, since the triangles BEF, BCA are similar, 
BE"" : BC" '.'. BEF : BCA. 
Wherefore, from equality of ratios, 

BEF : BCA : : m : n ; 

m 
and BEF=-xBGA. 

Eemark. The points E and F may easily be found 
by computation. 

For, since M^'^BCxBD, and BD = ~xBC, 



SEC. Ill] 



OF DIVIDING LAND. 



129 



BE'' = BG''x-',otBE 



we have 



In like manner BF= BA V — 

n 



= BG\f^. 



• EXAMPLE. 

Let it be required to divide tlie trian- 
gular field CAB, in whicli AG^'^ ch. AB = 
11 ell. and GB — 1 ch. into two sucli parts 
that ABE shall be one-fourth of the whole 
field. 

In this case, we have 

m = 1, w = 4, and " ' 




hence, 



AE-- 



n ^42 
4 ch. 50 1. and AB = b ch. 50 1. 



III. To run a line from a given point in the houndary of a 
piece of land, so as to cut off, on either side of the line, 
a given portion of the field. 

41. Make a complete survey of the field, by the rules 
already given. Let us take, as an example, the field whose 
area is computed at page 118. That field contains lOAA 
IB 16P, and the following is a plot of it. 




Let it now be required to run a line from station A, 
in such a manner as to cut off on the left any part of the 
field; say, 26A 2B 31P. 



130 ELEMEN-TS OF SURVEYING. [BOOK II. 

It is seen, by examining tlie field, that the division line 
will probably terminate on the course CD. Therefore, draw 
a line from A to G, which we will call the first closing 
line. 

The bearings and lengths of the courses AB, BO^ are 
always known ; and in the present example are found in 
the table on page 118 : hence, the bearing and distance 
from G to A, can be calculated by Art. 85: they are in 
this example, 

Bearing S 9° 28' E : Course 22.8 ch. 

Having calculated the bearing and length of the closing 
line, find, by the general method, the area which it cuts 
off: that area, in the present case, is 
13A ^R 3P. 

It is now evident that the division line must fall on 
the right of the closing line AC^ and must cut off an area 
ACH, equal to the difference between that already cut off, 
and the given area : that is, an area equal 

26.1 2R 31P given area, 

13^1 2>R 2>P area already cut off, 

to . . . 12^ 3i? 28P. 



Since the bearing of the next course GD, and the bear- 
ing of the closing line AG are known, the angle AGD 
which they form with each other, can be calculated, and is 
in this example 80° 32°. Hence, knowing the hypothenuse 
AG, and the angle AGG at the base, the length AG of 
the perpendicular let fall on the course GD, can be found, 
and is 22.49 chains. 

Since the area of a triangle is equal to its base multi- 
plied by half its altitude, it follows, that the base is equal 
to the area divided by half the altitude. Therefore, if the 

area 

12^ ZR 28P 
be reduced to square chains, and divided by 11.24^ chains, 
which is half the perpendicular A G, the quotient, which is 
11.58 chains, will be the base GK Hence, if we lay off 
from G, on GI), a distance Gff, equal to 11.58 chains, and 



SEC. IV.] PUBLIC LANDS. 131 

then run tlie line AH^ it will cut off from the land the re- 
quired area. 

Eemark I, If the part cut off by the first closing line, 
should exceed the given area, the division line will fall on 
the left of AG. 

Eemark II. If the difference between the given 
area and the first area cut off, divided by half the per- 
pendicular AG, gives ^ quotient larger than the course 
CD; then, draw a line from A to X>, and consider it as 
the first closing line, and let fall a perpendicular on DE. 

Remark III. When the point from which the divi- 
sion line is to be drawn, falls between the extremities 
of a course, dividing the course into two parts, con- 
sider one of the parts as an entire course, and the other 
as forming a new course, having the same bearing. The 
manner of making the calculation will then be the same 
as before. 



SECTION IV. 

PUBLIC LANDS — VARIATION" OF THE NEEDLE. 

1. Soon after the organization of the present govern- 
ment, several of the states ceded to the United States large 
tracts of wild land, and these, together with the lands since 
acquired by treaty and purchase, constitute what is called 
the public lands, or public domain. Previous to the year 
1802, these lands were parcelled out without reference to 
any general plan, in consequence of which the titles often 
conflicted with each other, and in many cases, several grants 
covered the same premises. 

In the year 1802, the following method of surveying 
the public lands, was adopted by Colonel Jared Mansfield, 
then surveyor-general of the North- Western Territory. 

2. The country to be surveyed is first divided by 
meridians, six miles distance from each other ; and then 



132 ELEMENTS OF SURVEYING. [BOOK II. 

again, by a system of east and west lines, also six miles 
from each other. The country is thus divided into equal 
squares, which are called townships. Hence, each township 
is a square, six miles on a side, and contains thirty-six 
square miles. 

3. For the purpose of illustration, we have obtained 
from the general land offi.ce the accompanying map, which 
represents a considerable portion of the State of Arkansas. 

The principal meridian in this Survey is called the 5th 
meridian, and passes through the point of junction of the 
White river and the Mississippi. The principal base line, 
running east and west, intersects this meridian a little to the 
east of White river ; and from the meridian and base line, 
reckoned from this point of intersection, all the ranges of 
townships are laid off. 

For example, 1 North, will apply to all the townships 
lying in the first row north of the base line : 1 South, will 
apply to all the townships in the first row south of the base 
hne. Eange 1 East, will apply to all the townships lying 
in the first row, east of the 5th meridian : and range 1 
West, will apply to all lying in the first row to the west 
of it. The small figures designate the rows of townships, 
reckoned north and south from the base line, and the 
ranges reckoned east and west from the 5th meridian. 
Thus, township 1 North, range 4 West, has its exact place 
designated, and may be immediately located. 

4. The principal meridians, and the principal base lines 
are established by astronomical observation, and the lines 
of subdivision run with the compass. 

For convenience in making surveys, and for the purpose 
of designating particular localities, a state or large tract, is 
often divided into parts called "Districts." There are three 
such districts in the map before us, the boundaries of which 
are designated by the full dark lines. 

5. Each township is divided into equal squares, by me- 
ridians one mile apart, and by east and west lines at the 
same distance from each other. Hence, each township is 
divided into 36 square miles, each one of which is called 



134 



ELEMENTS OF SURVEYING. [BOOK IL 



a section. The sections of a township are numbered from 
1 to 36, beginning at the north-east angle, and each con- 
tains 640 acres. 

The diagram exhibits the 36 sections of a township. 















6 


5 


4 


3 


2. 


1-- 


7 


8 


9 


10 


11 


12 


18 


17 


16 


15 


14 


13 


19 


20 


21 


22 


1 

23 


24 


30 


29 


28 


27 


26 


25 


31 


32 


33 


34 


35 


36 



To describe a section accurately, we say, section num- 
ber 5, in township number 4 north, in range 3d west of a 
known meridian ; the one, for example, drawn through the 
mouth of White river. The description fixes precisely the 
place of the section. Go to the 3d range of townships, 
west of the known meridian, find township number 4 north, 
in this range, and lastly, section number 5 of that town- 
ship. The corners of the sections should be marked bj 
permanent corner-posts, or by lines blazed on trees. 

6. The sections are divided into half sections, quarter 
sections, and even into eighths of sections. The following 
table shows the contents of a township, and its subdivi- 
sions : 

1 township = 36 sections = 23040 acres. 
1 section = 640 acres. 
i section = 320 acres. 
•^ section = 160 acres. 
\ section = 80 acres. 



SEC. IV.] VARIATION OF THE NEEDLE. 135 



VARIATION OF THE NEEDLE. 

7. The angle which the magnetic meridian makes with 
the true meridian, at any place on the surface of the earth, 
is called the variation of the needle at that place, and is east 
or west, according as the north end of the needle lies on 
the east or west side of the true meridian. 

8. The variation is different at different places, and 
even at the same place it does not remain constant for any 
length of time. The variation is ascertained by comparing 
the magnetic, with the true meridian. 

9. If we suppose a line to be traced through those 
points on the surface of the earth, where the needle points 
directly north, such a line is called the liiie of 7io variation. 
At all places lying on the east of this line, the variation 
of the needle is west ; at all places lying on the west of 
it, the variation is east. 

10. The public is much indebted to Professor Loomis, 
for the valuable results of many observations and much 
scientific research, on the dip and variation of the needle, 
contained in the 39th and 42d volumes of Silliman's 
Journal. 

The variation at each place was ascertained for the year 
1840 ; and by a comparison of previous observations and 
the application of known formulas, the annual motion, or 
change in variation, at each place, was also ascertained, and 
both are contained in the tables which follow. 

11. If the annual motion was correctly found, and con- 
tinues uniform, the variation at any subsequent period can 
be ascertained by simply multiplying the annual motion 
by the number of years, and adding the product, in the 
algebraic sense, to the variation in 1840. It will be ob- 
served that all variations west are designated by the plus 
sign ; and all variations east, by the minus sign. The an- 
nual motions being all west, have all the plus sign. 



136 



ELEMENTS OF SURVEYING. [BOOK II 



12. Our first object will be to mark tbe line, as it was 
in 1840, of no variation. For this purpose we sball make 
a table of places lying near this line. 



PLACES NEAE THE LINE OF NO VARIATION. 



Place. 


Latitude. 


Longitude. 


Variation. 


An. Motion. 


A Point. 


40° 53' 


80° 13' 


0° 00' 


+ 4'.4 


Cleveland, 0. 


41 31 


81 45 


-0 19 


4.4 


Detroit, Mich. 


42 24 


82 58 


-1 56 


4 


Mackinaw. 


45 51 


84 41 


-2 08 


3.9 


Marietta, 0. 


39 30 


81 28 


-1 24 


4.3 


Charlottesville, Ya. 


39 02 


78 30 


+ 19 


3.7 


Charleston, S. C. 


32 42 


80 04 


-2 44 


1.3 



At the point whose latitude is 40° 53', longitude 80° 
13', the variation of the needle was nothing in the year 
1840, and the direction of the line of no variation, traced 
north, was N 24° 35' west. The line of no variation, pro- 
longed, passed a little to the east at Cleveland, in Ohio — 
the variation there being 19 minutes east. Detroit lay still 
further to the west of this line, the variation there being 
1° 66' east; and Mackinaw still further to the west, as 
the variation at that place was 2° 08' east. 

The course of the line of no variation, prolonged south- 
erly, was S 24° 35' E. Marietta, in Ohio, was west of this 
line — the variation there being 1° 24' east. Charlottesville, 
in Virginia, was a little to the east of it — the variation there 
being 19' west ; whilst Charleston, in South Carolina, was on 
the west, — the variation there being 2° 44' east. 

From these results, it will be easy to see about where 
the line of no variation is traced in our own country. 

13. We shall give two additional tables: 



SEC. IV.] VARIATION OF THE NEEDLE. 



137 



PLACES WHERE THE VARIATION WAS WEST. 



Places. 


Latitude. 


Longitude. 


Variation. 


An. Motion. 


Angle of Maine. 


48° 


00' 


67° 


37' 


+ 19° 30' 


+ 8'.8 


Waterville, Me. 


44 


27 


69 


32 


12 36 


5.7 


Montreal. 


45 


31 


73 


35 


10 18 


5.7 


Keesville, N. Y. 


44 


28 


73 


32 


8 51 


5.3 


Burlington, Yt. 


44 


27 


73 


10 


9 27 


5.3 


Hanover, N. H. 


43 


42 


72 


14 


9 20 


5.2 


Cambridge, Mass. 


42 


22 


71 


08 


9 12 


5 


Hartford, Ct. 


41 


46 


72 


41 


6 58 


5 


Newport, E. I. 


41 


28 


71 


21 


7 45 


5 


Geneva, N. Y. 


42 


52 


77 


03 


4 18 


4.1 


West Point. 


41 


25 


74 


00 


6 52 


4 


New York City. 


40 


43 


71 


01 


5 34 


3.6 


Philadelpliia. 


39 


57 


75 


11 


4 08 


3.2 


Buffalo, N. Y. 


42 


52 


79 


06 


1 37 


4.1 



PLACES WHERE THE VARIATION WAS EAST. 



Places. 


Latitude. 


Longitude. 


Variation. 


An. Motion. 


Mouth, of Colum- 1 
bia Eiver. j 


46° 


12' 


123° 30' 


-2r 


40' 


Unknown. 


Jacksonville, 111. 


39 


43 


90 20 


8 


28 


+ 2'.5 


St. Louis, Mo. 


38 


37 


90 17 


8 


37 


2.3 


Nashville, Tenn. 


36 


10 


86 52 


6 


42 


2 


Louisiana, at 


29 


40 


94 00 


8 


41 


1.4 


Mobile, Ala. 


30 


42 


88 16 


7 


05 


1.4 


Tuscaloosa, Ala. 


33 


12 


87 43 


7 


26 


L6 


Columbus, Geo. 


32 


28 


85 11 


5 


28 


2 


Milledgeville, " 


33 


07 


83 24 


5 


07 


2.4 


Savannah, " 


32 


05 


81 12 


4 


13 


2.7 


Tallahassee, El. 


30 


26 


84 27 


5 


03 


1.8 


Pensacola, " 


30 


24 


87 23 


5 


53 


1.4 


Logansport, Ind. 


40 


45 


86 22 


5 


24 


2.7 


Cincinnati, 0. 

1 


39 


06 


84 27 


4 


46 


3.1 



138 



ELEMENTS OF SURVEYING. [BOOK II. 



METHODS OF ASCERTAINIKG THE VARIATION". 

14. The best practical metliod of determining the true 
meridian of a place, is bj observing the north star. If this 
star were precisely at the point in which the axis of the 
earth, prolonged, pierces the heavens, then, the intersection 
of the vertical plane passing through it and the place, with 
the surface of the earth, would be the true meridian. But, 
the star being at a distance from the pole, equal to 1° 30' 
nearly, it performs a revolution about the pole in a circle, 
the polar distance of which is 1° 30' : the time of revo- 
lution is 23 h. and 56 min. 

To the eye of an observer, this star is continually in 
motion, and is due north but twice in 23 h. 6Q min. ; and 
is then said to be on the meridian, Now, when it departs 
from the meridian, it apparently moves east or west, for 5 
h. and 59 min., and then returns to the meridian again. 
When at its greatest distance from the meridian, east or west, 
it is said to be at its greatest eastern or western elongation. 

The following tables show the times of its greatest 
eastern and western elongations : 

EASTERN ELONGATIONS. 



Days. 


April. 


May. 


June. 


July. 


August. 


Sept. 




H. M. 


H. M. 


H. M. 


H. M. 


H. M. 


H. M. 


1 


18 18 


16 26 


14 24 


12 20 


10 16 


8 20 


7 


17 56 


16 03 


14 00 


11 55 


9 53 


7 58 


13 


17 34 


15 40 


13 35 


11 31 


9 30 


7 36 


19 


17 12 


15 17 


13 10 


11 07 


9 08 


7 15 


25 


16 49 


14 53 


12 45 


10 43 


8 45 


6 53 



WESTERN ELONGATIONS. 



Days. 


Oct. 


Nov. 


Dec. 


Jan. 


Feb. 


March. 




H. M. 


H. M. 


H. M. 


H. M. 


H. M. 


H. M. 


1 


18 18 


16 22 


14 19 


12 02 


9 50 


8 01 


7 


17 56 


15 59 


13 53 


11 36 


9 26 


7 38 


13 


17 34 


15 35 


13 27 


11 10 


9 02 


7 16 


19 


17 12 


15 10 


13 00 


10 44 


8 39 


6 54 


25 


16 49 


14 45 


12 34 


10 18 


8 16 


6 33 



SEC. IV.] VARIATION OF THE NEEDLE. 



139 



The eastern elongations are put down from tlie first 
of April to the first of October ; and the western, from the 
first of October to the first of April ; the time is computed 
from 12 at noon. The western elongations in the first case, 
and the eastern in the second, occurring in the daytime, 
cannot be used. Some of those put down are also invisi- 
ble, occurring in the evening, before it is dark, or after day- 
light in the morning. In such case, if it be necessary to de- 
termine the meridian at that particular season of the year, 
let 5 h. and 59 min. be added to, or subtracted from, the time 
of greatest eastern or western elongation, and the observ- 
ation be made at night, when the star is on the meridian. 

15. The following table exhibits the angle which the me- 
ridian plane makes with the vertical plane passing through 
the pole-star, when at its greatest eastern or western elon- 
gation: such angle is called the azimuth. The mean angle 
only is put down, being calculated for the first of July of 
each year: 

AZIMUTH TABLE. 



Year. 


Lat. 32° 
Azimuth. 


Lat. 34° 
Azimuth. 


Lat. 36° 
Azimuth. 


Lat. 38° 
Azimuth. 


Lat. 40° 
Azimuth 


Lat. 42° 
Azimuth. 


Lat. 440 
Azimuth. 


1851 


1° 451' 


r48' 


1° 501' 


1° 53I' 


r 56f' 


2° 001' 


2° 041' 


1852 


1°45' 


1° 47i' 


1°50' 


1° 53' 


1° 561' 


1° 59f' 


2° 03|' 


1853 


1° 441' 


1°47' 


1° 49f' 


1° 521' 


1° 55|' 


1° 591' 


2° O31' 


1854 


l°44i' 


1° 461' 


1° 49i' 


1°52' 


r 551' 


1°69' 


2° 02|' 


1855 


1° 431' 


1° 461' 


1° 48f' 


1° 51f' 


l°54f' 


1° 581' 


2° 021' 


1856 


1° 43i' 


1° 45f' 


1° 481' 


r 511' 


l°54i' 


1°58' 


2° Olf 


1857 


1°43' 


1° 45i' 


1°48' 


1° 50f' 


1°54' 


1° 571' 


2° Oil' 


1858 


1° 42i' 


r 44|' 


r 471' 


1° 501' 


1° 531' 


1°57' 


2° OOf'l 


1859 


1°42' 


l°44i' 


1° 47/ 


1° 49f' 


1°53' 


1° 561' 


2° 001' 


1860 


1° 41f ' 


1°44' 


1° 46J' 


1° 491' 


1° 521' 


r 56' 


2° 00' 


1861 


1° 41i' 


r 431' 


1° 461' 


1°49' 


r 521' 


r 551' 


1° 59r 



140 ELEMENTS OF SURVEYING. [BOOK II, 

The use of tlie above tables, in finding tbe true meri- 
dian, will soon a,ppear. 



TO FIND THE TEUE MERIDIAN WITH THE THEODOLITE. 

16. Take a board, of about one foot square, paste wliite 
paper upon it, and perforate it through the centre ; the 
diameter of the hole being somewhat larger than the diam- 
eter of the telescope of the theodolite. Let this board be 
so fixed to a vertical stafi", as to slide up and down freely : 
and let a small piece of board, about three inches square, 
be nailed to the lower edge of it, for the purpose of hold- 
ing a candle. 

About twenty-five minutes before the time of the great- 
est eastern or western elongation of the pole-star, as shown 
by the tables of elongations, let the theodolite be placed 
at a convenient point and levelled. Let the board be 
placed about one foot in front of the theodolite, a lamp or 
candle placed on the shelf at its lower edge ; and let the 
board be slipped up or down, until the pole-star can be 
seen through the hole. The light reflected from the paper 
will show the cross hairs in the telescope of the theodolite. 

Then, let the vertical spider's line be brought exactly 
upon the pole-star, and, if it is an eastern elongation that 
is to be observed, and the star has not yet reached the 
most easterly point, it will move from the line towards the 
east, and the reverse when the elongation is west. 

At the time the star attains its greatest elongation, it 
will appear to coincide with the vertical spider's line for 
some time, and then leave it, in the direction contrary to 
its former motion. 

As the star moves towards the point of greatest elonga- 
tion, the telescope must be continually directed to it, by 
means of the tangent-screw of the vernier plate ; and when 
the star has attained its greatest elongation, great care 
should be taken that the instrument be not afterwards 
moved. 

Now, if it be not convenient to leave the instrument in 
its place until daylight, let a staff, with a candle or small 



SEC. IV.] VARIATION OF THE NEEDLE. 141 

lamp -apon its upper extremity, be arranged at thirty or 
forty yards from the theodolite, and in the same vertical 
plane with the axis of the telescope. This is easily effect- 
ed, by revolving the vertical limb about its horizontal axis 
without moving the vernier plate, and aligning the staff to 
coincide with the vertical hair. Then mark the point di- 
rectly under the theodolite ; the line passing through this 
point and the staff, makes an angle with the true meridian 
equal to the azimuth of the pole-star. 

From the table of azimuths, take the azimuth corres- 
ponding to the year and nearest latitude. If the observed 
elongation was east, the true meridian lies on the west of 
the line which has been found, and makes with it an angle 
equal to the azimuth. If the elongation was west, the 
true meridian lies on th§ east of the line: and, in either 
case, laying off the azimuth angle with the theodolite, gives 
the true meridian. 



TO FIND THE TEUE MERIDIAN WITH THE COMPASS. 

17. 1. Drive two posts firmly into the ground, in a line 
nearly east and west ; the uppermost ends, after the posts are 
driven, being about three feet above the surface, and the 
posts about four feet apart : then lay a plank, or piece of 
timber three or four inches in width, and smooth on the 
upper side, upon the posts, and let it be pinned or nailed, 
to hold it firmly. 

2. Prepare a piece of board four or five inches square, 
and smooth on the under side. Let one of the compass- 
sights be placed at right angles to the upper surface of the 
board, and let a nail be driven through the board, so that 
it can be tacked to the timber resting on the posts. 

3. At about twelve feet from the stakes, and in the 
direction of the pole-star, let a plumb be suspended from 
the top of an inclined stake or pole. The top of the pole 
should be of such a height that the pole-star will appear 
about six inches below it ; and the plumb should be swung 
in a vessel of water to prevent it from vibrating. 



142 ELEMENTS OF SURVEYING. [BOOK II. 

This being done, about twenty minutes before tbe time 
of elongation, place the board, to which the compass-sight 
is fastened, on the horizontal plank, and slide it east or 
west, until the aperture of the compass-sight, the plumb- 
line, and the star, are brought into the same range. Then 
if the star depart from the plumb-line, move the compass- 
sight, east or west, along the timber, as the case may be, 
until the star shall attain its greatest elongation, when it 
will continue behind the plumb-line for several minutes ; 
and will then recede from it in the direction contrary to 
its motion before it became stationary. Let the compass- 
sight be now fastened to the horizontal plank. During this 
observation it will be necessary to have the plumb-line 
lighted : this may be done by an assistant holding a candle 
near it. 

Let now a staff, with a candle or lamp upon it, be 
placed at a distance of thirty or forty yards from the 
plumb-line, and in the same direction with it and the com- 
pass-sight. The line so determined, makes, with the true 
meridian, an angle equal to the azimuth of the pole-star; 
and, from this line, the variation of the needle is readily 
determined, even without tracing the true meridian on the 
ground. 

Place the compass upon this line, turn the sights in the 
direction of it, and note the angle shown by the needle. 
Now, if the elongation, at the time of observation, was 
west, and the north end of the needle is on the west side of 
the line, the azimuth, plus the angle shown by the needle, 
is the true variation. But should the north end of the 
needle be found on the east side of the line, the elonga- 
tion being west, the difference between the azimuth and 
the angle would show the variation : and the reverse when 
the elongation is east. 

1. Elongation west, azimuth . . 2" 04' 
North end of the needle on the west, angle 4° 06' 

Variation 6° 10' west. 



SEC. IV.] VARIATION OF THE NEEDLE. 143 

2. Elongation west, azimuth . . 1° 59' 
North end of the needle on the east, angle 4° 50' 

Variation 2° 51' east. 



3. Elongation east, azimuth . . 2° 05' 
North end of the needle on the west, ande 8° 30' 



Variation 6° 25' west. 



4. Elongation east, azimuth . . 1° 57' 
North end of the needle on the east, angle 8° 40' 

Yariation 10° 37' east. 



Eemark I. The variation at West Point, in Septem- 
ber, 1835, was 6° 32' west. 

Remark II, The variation of the needle should al- 
ways be noted on every survey made with the compass, 
and then if the land be surveyed at a future time, the old 
lines can always be re-run. 

18. It has been found by observation, that heat and 
cold sensibly affect the magnetic needle, and that the same 
needle will, at the same place, indicate different lines at 
different hours of the day. 

If the magnetic meridian be observed early in the 
morning, and again at different hours of the day, it will 
be found that the needle will continue to recede from the 
meridian as the day advances, until about the time of the 
highest temperature, when it will begin to return, and at 
evening will make the same line as in the morning. This 
change is called the diurnal variation^ and varies, during 
the summer season, from one-fourth to one-fifth of a 
degree. 

19. A very near approximation to a true meridian, and 
consequently to the variation, may be had, by remember- 
ing that the pole-star very nearly reaches the true meri- 
dian, when it is in the same vertical plane with the star 
Alioth in the tail of the Great Bear, which lies nearest the 
four stars forming the quadrilateral. 



144 



ELEMENTS OF SURVEYING. [BOOK II. 



The vertical position can be ascer- 
tained by means of a plumb-line. To 
see the spider's lines in the field of the 
telescope at the same time with the 
star, a faint light should be placed 
near the object-glass. When the 
plumb-line, the star Alioth, and the 
north star, fall on the vertical spider's 
line, the horizontal limb is firmly 
clamped, and the telescope brought 
down to the horizon ; a light, seen 
through a small aperture in a board, i 

and held at some distance by an as- " 

sistant, is then moved according to signals, until it is cov- 
ered by the intersection of the spider's lines. A picket 
driven into the ground, under the light, serves to mark the 
meridian line for reference by day, when the angle formed 
by it and the magnetic meridian may be measured. 



,5*=-. 



~r" "v 



6 



BOOK III. 

LEVELLING AND TOPOGRAPHICAL SURVEnj^G. 



SECTION I. 

OF LEVELLING. 



1. Levelling is tlie art of determining tlie relative dis- 
tances of points from the centre of the earth. 

2. A line whose points are all equally distant from the 
centre of the earth, is called a line of true level, and a sur- 
face, all whose points are equally distant from the centre 
of the earth, as the surface of still water, is called a level 
surface. 

3. One point is said to be above another, when it is 
farther from the centre of the earth; and this difference of 
distance from the centre, is called the difference of level be- 
tween the two points. 

4. A straight line drawn tangent to a line of true level 
at any point, is a horizontal line, and is called a line of 
apparent level. Thus (PL 4, Fig. 1), if G is the centre of 
the earth and AEF a line of true level, ABD is a line of 
apparent level. This is the line of level determined by an 
instrument. The difference between the apparent and true 
level at any distant station _B, as determined from A, is BE, 
or the excess of the secant of the arc AE over the radius. 

5. To find a general formula for computing this excess, 
we have (Geom. B. IV., Prop. XXX.) 

AB'^ = BE {BE + 2EG)] 
but since the arc AE is very small in comparison with the 
10 



146 



ELEMENTS OF SURVEYING. [BOOK IIL 



radius of the eartli, tlie arc AE will not differ sensibly from 
tlie tangent AB ; tlie diameter 2JEC may, for the same 
reason, be taken for the secant {BE + 2EC) : hence, 



AH 



BUX2EC, or dividing by 2UG, 



BE= 



2EG 



(1). 



If we take the mean diameter of the earth to be 7919 

AE^" 
miles, formula (1) gives BE= WKTq (2) • lience, 

The departure of the apparent from the true level, starting 
from a given point, is equal to the square of the distance to the 
second point, divided hy the diameter of the earth. 

If in formula (2) you give to AE, in succession, every 
value from 1 chain to any given number of chains, (say 
100), and reduce at the same time both terms of the frac- 
tion to inches, a table may be comjDuted as below. 
Table showing the differences in inches between the true and ap- 
parent level, for distances between 1 and 100 chains. 



Chains. 


Inches. 


Chains. 


Inches. 


Chains. 


Inches. 


Chains. 


Inches. 


1 


.001 


26 


.845 


51 


3.255 


76 


7.221 


2 


.005 


27 


.911 


52 


3.380 


77 


7.412 


3 


.011 


28 


.981 


53 


3.511 


78 


7.605 


4 


.020 


29 


1.051 


54 


3.645 


79 


7.802 


5 


.031 


30 


1.125 


55 


3.781 


80 


8.001 


6 


.045 


31 


1.201 


56 


3.925 


81 


8.202 


Y 


.061 


32 


1.280 


57 


4.061 


82 


8.406 


8 


.080 


33 


1.360 


58 


4.205 


83 


8.612 


9 


.101 


34 


1.446 


59 


4.351 


84 


8.832 


10 


.125 


35 


1.531 


60 


4.500 


85 


9.042 


11 


.151 


36 


1.620 


61 


4.654 


86 


9.246 


12 


.180 


37 


1.711 


62 


4.805 


87 


9.462 


13 


.211 


38 


1.805 


63 


4.968 


88 


9.681 


14 


.245 


39 


1.901 


64 


5.120 


89 


9.902 


15 


.281 


40 


2.003 


65 


5.281 


90 


10.126 


16 


.320 


41 


2.101 


66 


5.443 


91 


10.351 


17 


.361 


42 


2.208 


67 


5.612 


92 


10.587 


18 


.405 


43 


2.311 


68 


5.787 


93 


10.812 


19 


.451 


44 


2.420 


69 


5.955 


94 


11.046 


20 


.500 


45 


2.531 


70 


6.125 


95 


11.233 


21 


.552 


46 


2.646 


71 


6.302 


96 


11.521 


22 


.605 


47 


2.761 


72 


6.480 


97 


11.763 


23 


.661 


48 


2.880 


73 


6.662 


98 


12.017 


24 


.Y20 


49 


3.004 


74 


6.846 


99 


12.246 


25 


.781 


50 


3.125 


75 


7.032 


100 


12.502 



SEC. 1] THE Y LEVEL. 147 

Observing tliat for AE— 80 chains = 1 mile, BE is equal 
to 8.001 inches, or about two-thirds of a foot, and since 
the differences of level vary as the squares of the dis- 
tances, we have the following easy rule for finding the cor- 
rection in feet. 

The correction for curvature^ in feet, is equal to two-thirds 
of the square of the distance in miles. 

INSTRUMENTS. 

6. Before proceeding further in the discussion of the 
principles of levelling, we will describe some of the in- 
struments used, and first, 

THE T LEVEL. 

7. A level is an instrument used to determine horizontal 
lines, and the difference of level of any two points on the 
surface of the earth. 

The part of the instrument shown in PL 4, Fig. 2, rests 
on a tripod, to which it is permanently attached at Z, HH 
is a horizontal brass plate, through which four levelling 
screws with milled heads are passed, and worked against a 
second horizontal plate OG. Two of these screws, K and 
ij are seen in the figure. aS' is a clamp-screw, which, being 
loosened, allows the upper part of the instrument to turn 
freely around its axis. Q is a tangent-screw, by means of 
which the upper part of the instrument is moved gently, 
after the clamp-screw S has been made fast. EE is a hori- 
zontal bar, perpendicular to which are the wyes, designat- 
ed Y's, that support the telescope LB. This telescope is 
confined in the Y's by the loops r, r, which are fastened 
by the pins p and p. The object-glass B, is adjusted to 
its focus by the screw X; the eye-glass L slides out and 
in freely. The screws f f work the slide which carries 
the horizontal hair ; and two horizontal screws, only one 
of which, a, is seen, work the slide that carries the verti- 
cal hair. CD is an attached spirit-level. The screw N 
elevates and depresses the Y, nearest the eye-glass. In 
some instruments this Y is elevated and depressed, by 
means of two screws at M and R. 



148 ELEMENTS OF SURVEYING. [BOOK IIL 

Before using this level, it must be adjusted. The ad- 
justment consists in bringing the different parts to their 
proper places. 

The line of collimation is the axis of the telescope. With 
this axis, the line drawn through the centre of the eye- 
glass and the intersection of the spider's lines, within the 
barrel of the telescope, ought to coincide. 

FlEST ADJUSTMENT.* To fix the intersection of the spider's 
lines in the axis of the telescojye. 

Having screwed the tripod to the instrument, extend 
the legs, and place them firmly. Then loosen the clamp- 
screw S^ and direct the telescope to a small, well-defined, 
and distant object. Then slide the eye-glass till the spider's 
lines are seen distinctly ; after Avhich, with the screw -Z", 
adjust the object-glass to its proper focus, when the object 
and the spider's lines will be distinctly seen. Note now 
the precise point covered by the intersection of the spider's 
lines. 

Having done this, revolve the telescope in the Y's, half 
round, when the attached level CD will come to the upper 
side. See if, in this position, the horizontal hair appears 
above or below the point, and in either case, loosen the 
one, and tighten the other, of the two screws which work 
the horizontal hair, until it has been carried over half the 
space between its last position and the observed point. 
Carry the telescope back to its place ; direct again, by the 
screws at M and i?, the intersection of the spider's lines to 
the point, and repeat the operation, till the horizontal hair 
neither ascends nor descends while the telescope is revolv- 
ed. A similar process will arrange the vertical hair, and 
the line of collimation is then adjusted. 

Second adjustment. To make the axis of the attached 
level CD parallel to the line of colliraation. 

Turn the screw N^ or the screws M and i?, until the 



* This, and some of the following adjustments, are so similar to those of the 
theodolite, that they would not be repeated, but that some may use the level 
without wishing to study a more complicated instrument. 



SEC. L] THE Y LEVEL. 149 

bubble of the level DO stands at the middle of the tube. 
Then open the loops, and reverse the telescope. If the 
bubble still stands at the middle of the tube, the axis of 
the level is horizontal ; but if not, it is inclined, the bubble 
being at the elevated end. In such case, raise the depress- 
ed, or depress the elevated end, by means of the screws M 
and h, half the inclination ; and then with the screw iV, 
bring the level to a horizontal position. Eeverse the teles- 
cope in the Y's, and make the same correction again ; and 
proceed thus, until the bubble stands in the middle of the 
tube, in both positions of the telescope; the axis of the 
level is then horizontal. * 

Let the telescope be now revolved in the Y's. If the 
bubble continues in the middle of the tube, the axis of the 
level is not only horizontal, but also parallel to the line of 
coUimation. If, however, the bubble recedes from the centre, 
the axis of the level is inclined to the line of collimation, 
and must be made parallel to it, by means of two small 
screws, which work horizontally ; one of these screws is 
seen at q. By loosening one of them, and tightening the 
other, the level is soon brought parallel to the line of col- 
limation ; and then, if the telescope be revolved in the Y's, 
the bubble will continue at the middle of the point of the 
tube. It is, however, difficult to make the first part of this 
adjustment, while the axis of the level is considerably in- 
clined to the line of collimation: for, allowing the level to 
be truly horizontal in one position of the telescope, after it 
is reversed, there will be but one corresponding position 
in which the bubble will stand at the middle of the tube. 
This suggests the necessity of making the first part of the 
adjustment with tolerable accuracy ; then, having made the 
second with care, re-examine the first, and proceed thus 
tin the adjustment is completed. 

Thirb adjustment. To make the level CD and the 
line of collimation perpendicular to the axis of the instruments 
or parallel to the horizontal har EE. 



Loosen the clamp-screw S, and turn the bar EE, until 
the level DG comes directly over two of the levelling 



150 ELEMENTS OF SURVEYING. [BOOK IIL 

screws. By means of these screws, make tlie level CD 
truly horizontal. Then, turn the level quite round ; if, 
during the revolution, it continue horizontal, it must be at 
right angles to the axis of the instrument about which it 
has been revolved. But if, after the revolution, the level 
CD be not horizontal, rectify half the error with the screws 
at M and i?, and half with the levelling screws. Then 
place the bar EE over the other two levelling screws, and 
make the same examinations and corrections as before ; and 
proceed thus, until the level can be turned entirely around 
without displacing the bubble at the centre. When this 
can be done, it is obvious that the level DC and the line 
of collimation, are at right angles to the axis of the instru- 
ment about which they revolve ; and since the axis is care- 
fully adjusted by the maker, at right angles to the bar EE^ 
it follows, that the line of collimation, the level DC^ and 
the bar EE, are parallel to each other. 

The level is now adjusted. When used, however, it is 
best to re-examine it every day or two, as the work will 
be erroneous unless the instrument is accurately adjusted. 

THE WATER LEVEL. 

8. The Water Level is an instrument that possesses the 
advantage of never requiring adjustment^ and also of being 
very cheap ; in fact, any ordinary workman may con- 
struct one. Having no telescope, it is impossible to take 
long sights, but for such work as is required to be done 
by the ordinary surveyor, it gives very good results. 

Two brass cups, G and i>, about four inches in diam- 
eter, and from four to five inches in height, are permanent- 
ly attached to a hollow brass tube of three feet long and 
half an inch in di- Q^ Fc 

ameter. The cups C*! 1^ 




are for the purpose ^ | ' 

of receiving the 

ends E and F of 

two bottles, the 

bottoms of which have been cut off. The bottoms may be 

cut off by tying a string round the bottles while heated. 

The ends are fixed in their places with putty. 



SEC. L] 



LEVELLING STAVES. 



151 



The projecting axis g works in a hollow cylinder h, 
which, forms the top of a stand. The tube, when the level 
is required for use, is filled with water (colored with lake 
or indigo), till it nearly reaches the necks of the bottles. 
After placing the stand tolerably level by the eye, with- 
draw both corks, and the surface of the water in the bot- 
tles will indicate a horizontal line in whatever direction the 
tube is turned. This level is well adapted to tracing con- 
tour lines as described in the next section. 



LEVELLING STAVES. 

9. The levelling staves are used to determine the points 
at which a given horizontal line intersects lines that are 
perpendicular to the surface of the earth, and to show the 
distances of such points of intersection from the ground. 

The levelling staff is a necessary accompaniment to 
either of the levels described. Several kinds are used. 

One of the best, consists of a staff 12 or 15 feet long, 
and graduated to feet, tenths, and hundredths. A sliding 
vane is made to move up or down by a 
cord and pulleys, and on the vane is a 
vernier, by means of which the reading 
of the staff may be effected to thou- 
sandths of an inch. . AB represents a 
portion of the staff, DG the moveable 
vane^ with an opening EF^ through which 
the graduation on the staff is seen. F is 
the vernier of the vane, the being de- 
termined by the transverse line DG. To 
render this line more distinct, the vane 
is divided into four quarters, and the 
alternate ones are painted black, which, 
by their contrast with the white quar- 
ters, ^show the line DG distinctly. 

10. Another variety of levelling staff is shown in PI. 4, 
Fig. 3. It is formed of two pieces, each about six feet 
long, one of which slides in a groove of the other, and 
bears a vane similar to that already described. It is grad- 
uated to feet, inches, and eighths of an inch. The line of 




162 ELEMENTS OF SURVEYING. [BOOK III. 

sight of the telescope is always directed to the centre of 
the vane. When the line of sight is less than six feet from 
the ground, the staff is reversed, — the vane run up the staff, 
and the readings made by means of the reversed figures at the 
right, where they are cut by the lower line of the vane. 
When the line of sight is more than six feet from the ground, 
the staff stands as in the figure, the reading is then made at 
the line he, and the figures indicating the height, are found on 
the sliding part which carries the vane. The reading of the 
staff, as it now stands, is seven feet. 

11. Another rod is sometimes used on which the figures 
are marked so plainly, that they may be read by the ob- 
server himself, without the aid of a vane ; thus avoiding 
errors through ignorance or negligence of the rodman. 

If the telescope used, inverts the object, the figures should 
be made inverted on the staff, so as to appear erect. Each 
of the rods described, has its advantages, and either one may 
be used according to the circumstances of the survey. 

12. There is a method of testing the adjustments of the 
Y level, which ought not to be neglected, since all the re- 
sults depend on the accuracy of the instrument. The 
method is this: 

The level being adjusted, place it at any convenient 
point, as G (Fig. 4). At equal distances of about 100 yards, 
on either side, and in the same line with the level, place 
the levelling staves, CE, BF. Make the level horizontal 
with the levelling screws. Then, turn it towards either 
staff, as BF, and run the vane up or down, as required, 
until the intersection of the hairs strikes the centre : then 
make the slide fast, and note carefully the height of the 
vane. Turn the level half round, and do the same in 
respect of the staff CE. 

Let the telescope be now reversed in the Y's. Sight 
again to the staff BF, and note the exact height of the 
vane. Let the telescope be now turned half round, and 
the same be done for the staff CE. If the two heights 
last observed, are equal to those first noted, each to each, 
the line of collimation is perpendicular to the axis of the 



SEC. L] OF LEVELLING. 153 

instrument, and if the bubble has, at the same time, pre- 
served its place at the middle point of the tube, the instru- 
ment is truly adjusted. 

For, had the line of coUimation b§en inclined to the 
axis of the level, it would, in the first instance, have taken 
the direction AF or Ad; and when turned half round, it 
would have taken the direction AU or Ab. The telescope 
being reversed in the Y's, and again directed to the staff 
BF, the line of collimation would take the direction Ad or 
AF, and when turned to the staff CF, it would take the 
direction Ab or AF: and the two distances BF, Bd, or (76, 
GE, can only be equal to each other when the line of col- 
limation falls on the horizontal line gf. 



LEVELLING IS THE FIELD. 

13. The operation of levelling may be undertaken: 

1st. For the purpose of determining the difference of 
level between two given points. 

2d. For the purpose of obtaining a section or profile 
along a given line, as in the- reconnoissance for a line of 
railroad. 

3d. For the purpose of determining the contour lines in 
a topographical survey, as described in the next section. 

DIFFERENCE OF LEVEL BETWEEN TWO POINTS. 

14. When it is proposed to find the difference of level 
of any two objects, or stations, all levels made in the di- 
rection of the station at which the work is begun, are 
called, for the sake of distinction merely, back-sights ; and 
levels taken in the direction of the other station, fore- 



Before going on the field with the level, rule three 
columns, as below, and head them, stations, back-sights, 
fore-sights. 



154 



ELEMENTS OF STJRVEYIN-G. [BOOK II] 



FIELD NOTES. 



Stations. 


+ Back-Sights. 


— Fore-Siglits. 


1 

2 
3 

4 


10 
11-6 

6-8 
3-9 


3 



4-9 

8-3 


Sums . . - - - HI -11 


16-0 




16-00 


Dif. of level . 


. . . 15-11 



EXAMPLE. 



Find the difference of level between any tiuo points^ as A and 
G (PI. 4, Fig. 5.) 

The level being adjusted, place it at any point, as B, as 
nearly in the line joining A and G as may be convenient. 
Place a levelling staff at Jl, and another at iV, a point 
lying as near as may be in the direction of G. Make the 
level horizontal, by means of the levelling screws ; turn the 
telescope to the staff at A^ and direct the person at the 
staff to slide up the vane until the horizontal line ah pierces 
its centre ; then note the distance Ah (equal to 10 feet in 
the present example), and enter it in the column of back- 
sights, opposite station 1. Sight also to the staff at iVJ and 
enter the distance Na, equal to 3 feet, in the column of fore- 
sights, opposite station 1. 

Take up the level, and place it at some other convenient 
station, as C, and remove the staff at A^ to M. Having 
levelled the instrument, sight to the staff at N^ and enter 
the distance Nd^ 11 feet 6 inches, in the column of back- 
sights, opposite station 2 : sight also to the staff at M^ and 
enter the distance Mf equal 0, in the column of fore-sights, 
opposite station 2. 



SEC. I.] OF LEVELLING. 155 

Let tlie level be now removed to any other station, as 
Z>, and tlie staff at iVJ to some otlier point, as P. Let tlie 
distance Mg^ equal to 6 feet 8 inches, be entered in the 
column of back-sights, opposite station 3, and the distance 
P/i, equal to 4 feet 9 inches, in the column of fore-sights. 
Let the instrument be now placed at E^ and the distance 
Pm, equal to 3 feet 9 inches, and On^ equal to 8 feet 3 
inches, be entered opposite station 4, in their proper 
columns. 

It is evident from the figure, that the difference of level 
NF^ between A and N^ is equal to the back-sight 6 J., dim- 
inished by the fore-sight aN] also that the difference of 
level between N and M is equal to the back-sight dN^ dim- 
inished by the foresight 0, and since each set of obser- 
vations is entirely independent of every other set, we may 
infer that the difference of level between two points as determin- 
ed hy one position of tlie level, is equal to the hack-sight^ dim- 
inished ly the fore-sight. If the fore-sight be greater than the 
back-sight, the difference will be affected with a minus sign, 
a result which shows that the second point is lower than 
the first. Generally, the difference of level betiveen any two 
points, detei^mined as above, is equal to the sum of the back- 
sights diminished by the sum of the fore-sights. If the result is 
plus, the second point is higher than the first ; if negative, 
it is lower. 

In the example given, the difference of level between 
A and G, is 15 feet 11 inches. 

15. In the previous example, we did not regard the dif- 
ference between the true and apparent level. If it be ne- 
cessary to ascertain the result with extreme accuracy, this 
difference must be considered : and then, the horizontal 
distances between the level, at each of its positions, and the 
staves, must be measured, and the apparent levels dimin- 
ished by the differences of level; which differences can be 
found from the table. 



156 



ELEMENTS OF SURVEYING. [BOOK IIL 



THE FOLLOWIlsrG IS SUCH AN" EXAMPLE. 



Stat. 


Back-sts. 


Distances. 


Fore-st. 


Distances. 


Cor.back-sights 


Cor. fore-sts. 


1 


9-8 


20 ch. 


1-6 


32 ch. 


9-7.500 


1-4.720 


2 


8-7 


25 ch. 


2-4 


28 ch. 


8-6.219 


2-3.019 


8 


5-2 


18 ch. 


3-1 


16 ch. 


5-1.595 


3-0.680 


4 


10-3 


29 ch. 


1-9 


87 ch. 


10-1.949 


0-11.538 


5 


11-0 


45 ch. 


2-5 


72 ch. 


10-9.469 


1-10.520 




44-2.732 


9-6.477 



In this example, the first column shows the stations ; 
the second, the back-sights; the third, the distances from 
the level in each of its positions to the back staff; the 
fourth, the fore-sights ; the fifth, the distances from the 
level to the forward staff; the sixth and seventh, are the 
colamns of back and fore-sights, corrected by the difference 
of level. The corrections are thus made : — The difference 
of level in the table corresponding to 20 chains, is 5 tenths 
of an inch, which being subtracted from 9 feet 8 inches, 
leaves 9 feet 7.5 inches for the corrected back-sights; this 
is entered opposite station 1 in the sixth column. The dif- 
ference of level corresponding to 32 chains, is 1.280 inches, 
which being subtracted from the apparent level, 1 foot 6 
inches, leaves 1 foot 4.720 inches for the true fore-sight 
from station 1. The other corrections are made in the 



same manner. 



The sum of the back-sights being 44 feet 2.732 inches, 
and the sum of the fore-sights 9 feet 6.477 inches, it fol- 
lows, that the difference, 34 feet 8.255 inches, is the true 
difference of level. 

16. In finding the true from the apparent level, we 
have not regarded the effect caused by refraction on the 
apparent elevation of objects, as well because the refraction 
is different in different states of the atmosphere, as because 
the corrections are inconsiderable in themselves. 

17. The small errors that would arise from regarding 
the apparent as the true level, may be avoided hy placing 



SEC. I.] OF LEVELLING. 157 

the levelling staves at equal distances from the level. In such, 
case, it is plain, 1st, tliat equal corrections must be made 
in the fore and back-sights; and, 2dly, that when the fore 
and back-sights are diminished equally, the result, which is 
always the difference of their suras, will not be affected. 

This method should always be followed, if practicable, 
as it avoids the trouble of making corrections for the dif- 
ference of true and apparent level. 

The differences between the true and apparent level, 
being very inconsiderable for short distances, if only ordi- 
nary accuracy be required, it will be unnecessary to make 
measurements at all. Care, however, ought to be taken, 
in placing the levelling staves, to have them at as nearly 
equal distances from the level as can be determined by the 
eye ; and if the distances are unequal, let the next distances 
also be made unequal; that is, if the back-sight is the 
longer in the first case, let it be made proportionably 
shorter in the second, and the reverse. 

LEVELLING FOR SECTION". 

18. Having decided upon the line along which a section 
is to be taken, let a permanent mark be made at the be- 
ginning of the line : this is called a hench-mark. A bench- 
mark is made by drilling a hole in a rock, or by painting 
upon a rock or fence, or sometimes by driving a stake in 
the ground, with its upper end marked by a nail-head. 
Bench-marks should be made from time to time along the 
line, to serve as checks, in case a re-survey should become 
necessary. 

The operations in the field are similar to those in the 
last example, and the field notes are kept in the same 
manner, except that a new column is added for bearings, 
when it is necessary to make a plot of the line of survey. 
The total distance of each point above or below the start- 
ing point may be computed, and written in a separate col- 
umn, paying particular attention to the signs. We annex 
an example, in witiich the heights are estimated in feet, 
and decimals of a foot. 



15i 



ELEMENTS OF SURVEYING. [BOOK III. 



sta- 
tion. 


DiBtances in 
feet. 


B. Sight. 


F. Sight. 


Dif. between 
B. S. and F. S. 


Total Dif. of 
Level. 


REMARKS. 


1 


650 


2.35 


14.55 


-12.20 


- 12.20 


Commenced at bench-mark A. 


2 


700 


3.56 


9.58 


- 6.02 


-18.22 




3 


750 


10.34 


6.21 


+ 4.13 


- 14.09 




4 


650 


14.55 


0.25 


+ 14.30 


+ 0.21 




5 


600 


9.98 


1.67 


+ 8.31 


+ 8.52 




6 


650 


3.62 


14.54 


- 10.92 


- 2.40 






B.M 


1.23 


13.45 


- 12.22 


- 14.62 


Bench-mark on rock. 


7 


500 


2.23 


12.05 


- 9.82 


- 24.44 


Terminating xABMon oak tree. 


8 


750 


6.20 


19.55 


- 13.35 


- 37.79 





The fiftli column shows the diiference of level between 
any two consecutive positions of the levelling staff, and is 
found by subtracting the fore-sight from the corresponding 
back-sight, and giving to the remainder the proper sign. 
The sixth column shows the distance of each point above 
or below the bench-mark J., and is obtained by continual 
additions of the numbers in column 5. Thus, 
(- 12.20) -f (- 6.02) = - 18.22 ; (- 18.22) + 4.13 = - 14.09 ; 
and so on. 

It will be seen that the point of termination is 37.79 
feet below the starting point. 



PLOTTING THE SECTION OR PROFILE. 

19. The vertical distances being generally very small as 
compared with the horizontal distances, two different scales 
become necessary in plotting a profile. In order that the 
vertical distances may be fully exhibited in the plan, the 
scale used for them is much larger than is used for lines 
measured in a horizontal direction. This becomes absolutely 
necessary where long lines of profile, with a gentle slope, 
are to be plotted, as is always the case in the trial section 
of a railroad survey. "We shall illustrate the manner of 
plotting, by drawing the section determined by the field- 
notes just given. 

20. Draw a horizontal line AK^ called a datum line, and 



SEC. II.] TOPOGRAPHICAL SURVEYING. 



159 



assume some point as A, to represent tlie point of begin- 
ning: lay off on tlie datum line, distances equal to tlie 



A 650 B 700 C 750 J) 650 



(1) %v ^- 




'^^%^0€ 



(3) 



<?oOO H 750 K 

I 




measured distances 650, 700, 750, &c., feet to K, using in 
this case a scale of 1500 feet to 1 incli. At tlie points B, 
C, Z>, JE, &c., tlius determined, erect perpendiculars, making 
them equal, on a scale of 25 feet to the inch, to the cor- 
responding differences of level taken from the field-book; 
through the points thus found, draw the irregular line 
APLM, and it will represent the surface of the ground 
along the line of level. 

The bench-mark, between stations 7 and 8, is not plotted, 
as it is supposed to be out of the line of the section, and 
no distances are measured to it. 



SECTION II. 

TOPOGRAPHICAL SURVEYING. 

21. Besides the surveys that are made to determine the 
area of land and the relative positions of objects, it is fre- 
quently necessary to make minute and careful examinations 
for the purpose of ascertaining the form and accidents of 
the ground, and to make such a plan as will distinguish 
the swelling hill from the sunken valley, and the course 
of the rivulet from the unbroken plain. 



160 ELEMENTS OF SURVEYING. [BOOK III 

22. This brancb. of surveying is called Topography. In 
surveys made with a view to the location of extensive 
works, the determination of the slopes and irregularities of 
the ground is of the first importance : indeed, the examina- 
tions would otherwise be useless. 

23. The manner of ascertaining these irregularities is, to 
suppose the surface of the ground to be intersected by a 
system of horizontal planes at equal distances from each 
other ; the curves determined by these secant planes, being 
lines of the surface, will indicate its form at the places of 
section, and, as the planes are nearer or more distant from 
each other, the form of the surface is more or less accu- 
rately ascertained. 

If such a system of curves be determined, and then pro- 
jected or let fall on a horizontal plane, it is obvious that 
the curves on such plane will be nearer together or farther 
apart, as the ascent of the hill is steep or gentle. 

If, therefore, such intersections be made, and the curves 
so determined be accurately delineated on paper, the map 
will give such a representation of the ground as will 
show its form, its inequalities, and its striking character- 
istics. 

24. The subject divides itself, naturally, into two parts. 

1st. To make the necessary examinations and measure- 
ments on the field ; and, 

2d. To make the delineations on paper. 

For the former of these objects, the theodolite is the 
best instrument; the common level, however, will answer 
all the purposes, though it is less convenient. 

Before going on the field, it is necessary to provide a 
number of wooden stakes, about two feet in length, with 
heads. These stakes are used to designate particular points, 
and are to be driven to the surface of the ground. A 
nail should then be driven into the head of each of them, 
to mark its centre. 

25. "We shall, perhaps, be best understood, by giving an 
example or two, and then adding such general remarks as 



SEC. IL] TOPOGRAPHICAL SURVEYING. 161 

will extend tlie particular cases to all others that can 
occur. 

Let A (PL 4, Fig. 6), be the summit of a hill, the con- 
tour of which it is required to represent. At A, let a 
stake be driven, and let the axis of the theodolite, or level, 
be placed directly over the nail which marks its centre. 
From A, measure any line down the hill, as AB, using the 
telescope of the theodolite or level to arrange all its points 
in the same vertical plane. Great care must be taken to 
keep the measuring chain horizontal, for it is the horizontal 
distances that are required. At different points of this line, 
as a, 5, c, c?, &c., let stakes be driven, and let the horizon- 
tal distances J.a, aS, 5c, and cd^ be carefully measured. In 
placing the stakes, reference must be had to the abruptness 
of the declivity, and the accuracy with which the surface 
is to be delineated: their differences of level ought not to 
exceed once and a half, or twice, the distance between the 
horizontal planes of section. 

Having placed stakes, and measured all the distances 
along the line AB, run another line down the hill, as AG, 
placing stakes at the points e, / g, and A, and measuring 
the horizontal distances Ae, ef, fg, and gh. Run also the 
line AD^ placing stakes at «, Z, m, and n, and measuring 
the horizontal distances Ai, il, Im, and mn. 

Each line, AB, A C, AD, running down the hill from A, 
may be regarded as the intersection of the hill by a verti- 
cal plane ; and these secant planes are to be continued over 
all the ground which is to be surveyed. K the work is 
done with a theodolite, or with a level having a compass, 
the angles DAB and BAG, contained by the vertical se- 
cant planes, can be measured; if it is done with a level, 
having no needle, let any of the distances ae, hf, ai, hi, &c., 
be measured with the chain, and there will then be known 
the three sides of the triangles Aae, Abf, Aai, Ahl, &c. 

Let now, the difference of level of the several points 
marked in each of the lines AB, AD, AG, be determined. 

In the present example the results of the measurements 
and levelling, are — 

11 » 



ELEMENTS OF SURVEYING. [BOOK IIL 



Line AB. 



Distances. 
Aa = 40 feet 
ah =50 " 
he =30 " 
cd =46 " 

Distances. 
Ae = 28 feet 
ef =45 " 
fg =55 " 
gh =49 " 



Distances. 
Ai = 25 feet 
il = 55 " 
Im =38 " 

mn = 48 " 



Line AC. 



Line J.i). 



Difference of Level. 
A above a 12 feet 
a above 5 8" 
h above c 9 " 
c above d 11 " 

Difference of Level. 
A above e 11 feet 
e above / 9 " 
/ above ^ 12 " 
g above ^ 14 " 

Difference of Level. 
A above i 9 feet 
i above I 13 " 
Z above w 7 " 
m above n 14 " 

30°. 



Angle CL4J5= 25°, AnglQ DAB ■ 

Tbese data are sufficient, not only to find the intersec- 
tions of horizontal planes with the surface of tbe bill, but 
also for delineating sucb curves of section on paper. 

Having drawn on tbe paper tbe line AB, lay off tbe 
angle BAG=2b°, and the angle BAD = ZO°. Then, from 
a convenient scale of equal parts, lay off tbe distances Aa, 
ah, he, cd, Ae, ef, fg, gh, Ai, il, Im, and mn. 

Let it be required that tbe borizontal planes be at a 
distance of eigbt feet from eacb otber. Since A is tbe 
bigbest point of tbe bill, and tbe difference of level of tbe 
points A and a, is 12 feet, tbe first plane, reckoning down- 
wards, will intersect tbe line traced on tbe ground from A 
to B, between A and a. Eegarding tbe descent as uniform, 
wbicb we may do for small distances without sensible error, 
we have this proportion ; as the difference of level of the 
points A and a, is to the horizontal distance Aa, so is 8 
feet, to the horizontal distance from A to where the first 



SEC. II.] TOPOGRAPHICAL SURVEYING. 163 

horizontal plane will cut the line from A to B. This dis- 
tance being thus found, and laid off from A to o, gives o, 
a point of the curve in which the first plane intersects the 
ground. The points at which it cuts the line from A to C, 
and the line from A to i), are determined similarly, and 
three points in the first curve are thus found. 

The graphic operations are greatly facilitated by the aid 
of the sector. Let it be borne in mind, that the descent 
from A to a, is 12 feet, and that it is required, upon the 
supposition of the descent being uniform, to find that part 
of the distance corresponding to a descent of 8 feet. Take 
the distance from A to a, in the dividers, and open the 
arms of the sector until the dividers will reach from 12 on 
the line of equal parts, on one side, to 12 on the line of 
equal parts, on the other. Then, without changing the 
angle, extend the dividers from 8 on one side, to 8 on the 
other; this will give the proportional distance to be laid 
off from A to o. Or, if the dividers be extended from 4 
to 4, the proportional distance may be laid off from a 
to 0. 

If the distances to be taken from the sector fall too 
near the joint, let multiples of them be used ; as for in- 
stance, on the French sectors, let the arms be extended 
until the dividers reach from 120 on the one, to 120 on 
the other, then 80 or 40 will be the proportional numbers. 
Other multiples may be used, though it is generally more 
convenient to multiply by 10. 

26. The second plane is to pass 8 feet below the first, 
that is, 16 feet below J., or 4 feet below a, a being 12 feet 
below A. Take the distance ah in the dividers, and ex- 
tend the sector, so that the dividers will reach from 8 to 
(the descent from a to 6 being 8 feet) 8, or fi-om 80 to 
80 ; then, the distance from 4 to 4, or from 40 to 40, being 
laid off from a to ^, gives p, a point of the second curve. 

The difference of level between a and h being 8 feet, 
and the difference of level between a and ^ being 4 feet, 
the difference of level between 'p and h must also be 4 
feet; hence, the third plane will pass 4 feet below 6, and 



164 



ELEMEITTS OF SURVEYING. [BOOK III. 



q, determined as above, is a point of the third curve, and 
so on. After having determined the points in which each 
contour line cuts the lines diverging from J., let the con- 
tour lines be drawn through them, so as to indicate the 
surface of the hill. The numbers (8), (16), &c., show the 
vertical distances of the respective planes below the point A. 

27. Having drawn the horizontal curves, the next thing 
to be done is so to shade the drawing that it may represent 
accurately the surface of the ground. This is done by 
drawing a system of small broken lines, as in the figure, 
perpendicular in direction to the horizontal curves already 
described. In all topographical representations of undulat- 
ing ground, the lines of shading are drawn perpendicular to 
the horizontal curves. 

A profile along either of the diverging lines may be 
plotted by the rules already given (Art. 20.) The diagram 
shows the profile along the line AB. 




28. The following example will illustrate the methods 
employed in making a topographical survey, where great 
accuracy is required. 



By means of a theodolite or level, range a line of stakes 
A, B, C, D, E^ kc, along one side, or through the middle of 
the ground to be surveyed, at equal and convenient distances 
from each other, say 50 feet apart. Mark, with a piece of 
red chalk, on each stake in this row, one of the letters of 
the alphabet. A, B, 0, D, B, &c., in their order. At A, 
range a line of stakes, perpendicular to AB, planting the 
stakes at intervals of 60 feet ; and mark them with the 
letters ^j ^j ^j &c., which are read A first, A second, 
A third, &c. 



SEC. II.] TOPOGRAPHICAL SURVEYING. 



165 



B 



E 



A 
1 


A 


A 

3 


A A 

4 S 


B 
1 


B 

2r 


B 

3 

b 


B B 

4 


c 

1 


c 

z 


(' 
3 


c a 

4 S 


D 

1 

El 


B- 


D 
s 

a 
us 


B V 

4 S 

E4 Ss 



At B, range a line of stakes also perpendicular to AE, 
and at distances of 50 feet from eacli other, and designate 
them ^j ^j -^> &c. Do the same at G, D, E, &c., until all 
the stakes are placed, dividing the area to be surveyed 
into squares of 50 feet on a side. The letters and figures 
should be plainly marked on a smooth face of each stake, 
for facility of reference. If this system of notation be fol- 
lowed, the stakes may be recorded without danger of con- 
fusion. 

The next operation is to determine the difference of 
level between each stake, and some fixed horizontal plane, 
which is called a ^lane of reference. If the sea is near, the 
plane of mean low water, may be taken as the plane of 
reference. If not, assume the horizontal plane, passing 
through the lowest point of the ground to be surveyed, and 
make a permanent bench-mark at the point of beginning. 
If the lowest point cannot be easily determined, assume 
such a plane of reference as shall pass quite below the low- 
est point of the ground. 

In the example, which we have taken for illustration, 
the stake -^» is at the lowest point, and let us assume the 
plane of reference to pass through that point. 



166 



ELEMENTS OF SIIRVEYIIfG. [BOOK IIL 



Set up the level at some convenient point, as a, take tlie 
reading of a levelling staff, set up at -^j and enter this 
reading as a back-sight. Then take the readings of the 
staff, at as many stakes as « can be reached from the posi- 
tion a of the level, entering them as fore-sights. Endeavor- 
ing to make the last reading as small as possible. At this 
last stake ^' drive a small peg for a bench-mark. 

Move the level to a second point b, and take a back- 
sight to the bench-mark (Gi), and fore-sights, to as many 
stakes as possible. The following is the form of a field- 
book, used in topographical levelling. 



FIELD NOTES. 



Back-sights. 


Fore-Sights. 


Difference 


Total dif.of level 
above E 3 


Remarks. 


Object 


Reading 


Object 


Reading 




Object 
E3 


Reading 
0.000 




E3 


11.432 


D3 


1.211 


-f 10.221 


D3 


10.221 








C4 


0.897 


-F 0.314 


C4 


10.535 


Check 10.535 


C4 


11.112 


E2 


5.281 


+ 5.831 


E2 


16.366 








E4 


6.154 


— 0.873 


E4 


15.493 








D4 


6.001 


-1- 0.153 


D4 


15.646 








D2 


1.182 


+ 4.819 


D2 


20.465 








C3 


2.917 


— 1.735 


C3 


18.730 








B5 


6.080 


— 3.163 


B5 


15.567 








C5 


0.921 


-1- 5.159 


C5 


20.726 








B4 


0.113 


-1- 0.808 


B4 


21.534 


Check 10.999 


B4 


11.882 


El 


8.019 


-f 3.863 


El 


25.397 


21.534 






B3 


3.990 


+ 4.029 


B3 


29.426 








Dl 


4.118 


— 0.128 


Dl 


29.298 








C2 


1.880 


-1- 2.238 


C2 


31.536 








A4 


5.000 


— 3.120 


A4 


28.416 








A5 


9.928 


— 4.928 


A5 


23.488 








D5 


1.675 


+ 8.253 


D5 


31.741 








E5 


1.111 


+ 0.564 


E5 


82.305 








A3 


0.108 


+ 1.003 


A3 


33.308 








CI 


0.004 


-f- 0.104 


CI 


83.412 


Check 11.878 


CI 


11.149 


B2 


4.181 


+ 6.968 


B2 


40.380 


33.412 






Bl 


2.008 


+ 2.173 


Bl 


42.553 








A2 


0.817 


+ 1.191 


A2 


43.744 


Check 10.832 
43.744 


A2 


10.102 


Al 


4.332 


-i- 5.770 


Al 


49.514 


Check 5.770 
















49.514 



SEC. II.] TOPOGRAPHICAL SURVEYING. 167 

If we subtract the first fore-sight (D3), from the back- 
sight (E3), the difference, entered in the column headed 
difference^ is evidently the height of (D3), above the plane 
of reference through (E3); and we accordingly enter it 
under the column headed total diff. of level, as well as in 
the column of differences. If we subtract the fore-sight 
(C4) from the fore-sight (D3), the difference, entered in the 
column of difference, is evidently the height of (C4) above 
(D3); if we now add this difference to the previous total, 
we shall find the height of (C4) above (E3). Subtracting 
the fore-sight (E2) from the back-sight (C4), we get the dif- 
ference of level between (E2) and (04) which, added to the 
previous total, gives the height of (E2), above the stake 
(E3). In subtracting the fore-sight (E4) from the fore-sight 
(E2), we find a negative result which shows that (E4) is 
below (E2). We enter, then, this difference with its neg- 
ative sign, and to get the total, we subtract this difference 
from the previous total, and so on. 

As a check on the accuracy of our computation, sub- 
tract the fore-sight (C4) from the back-sight (E3), and the 
difference will give the height of (C4), above the plane of 
reference. 

Again, subtract the fore-sight (B4) from the back-sight 
(C4), and add the remainder to the height of (C4,) and we 
shall find the height of (B4), which should agree with the 
height found under the heading, total diff. of level; and so 
on for each time the level is moved. 



PLOTTING THE WORK. 

29. Draw, on a piece of paper, a straight line AW. 
From a scale of equal parts, set off distances AB, BG, 
&c., each to. represent 50 feet. Erect perpendiculars at 
each of the points A, B, 0, &c., and then set off the distan- 
ces from A to 2, from 2 to 3, &g., each to represent 50 
feet; and through the points 2, 3, 4 and 5, draw parallels 
to AB. These, by their intersections with the lines drawn 
through A, B, (7, &c., will determine the position of the 
stakes, 4' ^' &c.: and write in red ink on the plot, the 



168 ELEMEN-TS OF SURVEYING. [BOOK IIL 

height above the plane of reference of each stake, taken from 
the column of total differences in the field-book. Let us sup- 
pose that the horizontal planes are to be taken at distances 
of 6 feet. We may find the points in which the contour 





19.5 / \l7 , ^ 


33.-5 1 428,4 ,5 


\-'^ 


40,4 / 


J / 


21,5 X 






.«/ / 


■^) 1 


C 
D 
K 


331- 


29,3 / 


/ / 

/ / 

30,5 / / 




/ 1 
f 1 

15.6 / / , 


J/ 


/' J 

16,4./ / 


0,0 ) 


\\\ 

1.^.5 / \ 



lines intersect the lines at right angles, by the previous 
method, or perhaps still better, let the Surveyor take the 
plot thus commenced into the field, and by the eye trace 
the contour lines on the map. If we note where the lines 
at right angles cut fences, roads, streams, &c., we can, by 
joining the points, obtain a plot of the ground. 

80. The contour lines may be found as follows : Set up 
the level at a, and observe that the back-sight, to the stake, 
placed at (.^3), gave a reading of 11.432. Depress the 
vane equal to the distance between the horizontal secant 
planes, that is, 6 feet, which is done by placing it. at the 
reading 5.432. Then direct the rodman, by signals up or 
down the hill, till the horizontal hair of the telescope coin- 
cides with the horizontal line of the vane. The foot of the 
staff is then 6 feet above the first point. Let a stake, 
marked 6, be driven here, and direct the rodman around 
the hill, until a second position shall be found, when the 



SEC. II.] TOPOGRAPHICAL SURVEYING. 



169 



horizontal liair of the telescope will cut the vane, and drive 
there another stake, marked 6 ; and so on, until a sufficient 
number of stakes have been driven to determine the curve 
(6). Then, let the line of stakes, marked 6, be surveyed 
with the compass and chain, and plotted. Other contour 
lines may be found in a similar manner, 

31. We will add another example for determining the 
contour of an undulating piece of ground (PL 4, Fig. 
7,) by means of horizontal sections. Let rows of stakes 
DA^ HE^ IF^ &c., be driven at intervals, depending upon 
the required accuracy of the survey, and let / g, h, &c., 
be stakes driven along the lines, at such points as will 
best show the accidents of ground. Determine as before 
the difference of level between each stake, and some fixed 
point, and then determine where the contour lines cut the 
lines AD, JEH, &c., by the rules already laid down. 

After the stakes are all placed, and the distances meas- 
ured, let the differences of level of all the points so desig- 
nated be found. In the present example, the results of the 
measurements are, 



Ft. 


Ft. 


Ft. 


Ft. 


Ft. 


Aa =80 


AE= 100 


EF= 100 


FG = 100 


GD=100 


ab =60 


Ef =105 


Fi = 74 


Gm= 96 


Bq = 76 


he =90 


fg = 85 


ik =115 


mn = 76 


qs = 85 


cd =55 


gh = 71 


M = 60 


np = 76 


St = 127 


dD = bO 


hH= 74 


II = 86 


pL = 87 


tG = 47 


Of the Levelling. 


Line AD. 


Line EH. 


Line FI. 


Line ai. 


Line BG. 


Ft. 


Ft. 


Ft. 


Ft. 


Ft 


A above a 5 


^below J. 3 


i^'below E 2 


6^belowi^l 


^below6^2 


a '' bQ 


^above /9 


i'^ above ^ 3 


G above m 2 


jS above q 3 


b " c 7 


/ " ^3 


i " Z;5 


w " wl 


q "52 


C below d 2 


g '' hi 


k '' 12 


n '' p2 


S " ^3 


d above Z) 4 


hhelovfUS 


I below IB 


p below Z 4 


t below (75 



The heights of the points are here compared with each 
other, two and two. Before, however, we can conceive 



170 



ELEMENTS OF SURVEYING. [BOOK III. 



clearly their relative lieiglits, we must assume some one 
point, and compare all the others with it. Let the point 
A be taken. The height of 

Ft. Ft. 

J. above a 5 ^ above/ 12 J. above ^ 13 J. above j9 11 



A 


' I 11 


A 


A 


" c 18 


A 


A 


" d 16 


A 


A 


' i)20 


A 


A 


' E 3 


A 



g 15 
h 16 
^13 

F 5 

i 8 



A " Z 15 

A " / 12 

^ " (^ 6 

A " m 8 

^ " w 9 



A 


" L 7 


A 


" B 8 


A 


" q 11 


A 


" s 13 


A 


" t 16 



J.nd of J. above (7, 11 feet. 

This being done, a mere inspection shows us the high- 
est and lowest points, as also the relative heights of the 
others, reckoning upwards or downwards. Let them be 
now written in the order of their heights above the lowest 
point, which is D. The difference of level between A and 
D being 20 feet, if the difference of level of each of the 
points below J., be taken from 20 feet, the remainder will 
be the height above D. Arranging them in their order, 
we have 



Ft 

above D 2 


" D 4 


" D 4 


" D 4: 


" D 5 


" D 5 



^above D 7 



" D 7 
" X> 7 
" D 8 
" D 8 
" D 9 
A above I). 





Ft. 1 


2) above D 9 


9 


" D 9 


G 


" X> 9 


n 


" Dll 


i 


" D12 


m 


" Z>12 



^abovei^l2 



X>14 

D15 
DVl 



20 feet. 



In this example, the plane of reference is assumed 
through D, the lowest point of the ground ; and the secant 
planes are taken 3 feet apart. 

82. The manner of shading the map, so as to indicate 
the hills and slopes, consists in drawing the lines of shad- 
ing perpendicular to the horizontal curves, as already ex- 
plained. These shading lines are drawn close together, 
when the slope is abrupt, and further apart, as it grows 
more gentle. Fig. 7 indicates the method of shading. 



SEC. II.] TOPOGRAPHICAL SURVEYING. 171 

83. Wlien the plane of reference is so chosen that the 
points of the work fall on different sides of it, all the re- 
ferences on one side are called positive, and those on the 
other, negative. The curves having a negative reference 
are distinguished by placing the minus sign before the 
number ; thus — ( ). 

34. In topographical surveys, great care should be taken 
to leave some permanent marks, with their levels written 
on them in a durable manner. For example, if there are 
any rocks, let one or more of them be smoothed, and the 
vertical distance from the plane of reference marked there- 
on: or let the vertical distance of a point on some promi- 
nent building, be ascertained and marked permanently on 
the building. Such points should also be noted on the 
map, so that a person, although unacquainted with the 
ground, could by means of the map, go upon it, and trace 
out all the points, together with their differences of level. 

35. Besides representing the contour of the ground, it 
is often necessary to make a map which shall indicate the 
cultivated field, the woodland, the marsh, and the winding 
river. For this, certain characters, or conventional signs, 
have been agreed upon, as the representatives of things, 
and when these are once fixed in the mind, they readily 
suggest the objects for which they stand. Those which 
are given in Plates 5 and % have been adopted by the 
Engineer Department, and are used in all plans and maps 
made by the United States Engineers. 

It is very desirable that a uniform method of deline- 
ation should be adopted, and none would seem to be of 
higher authority than that established by the Topographi- 
cal Bureau. It is, therefore, recommended, that the con- 
ventional signs given in Plates 5 and 6, be carefully 
studied and uniformly followed. 



BOOK IV. 

GEODESIC, TEIGONOMETEIC AND MAEITIME 
SUEYEYING. 



SECTION I. 

GEODESIC AND TEIGONOMETRIO SURVEYnTG. 

1. When a large extent of territory, or a long line of 
sea-coast is to be surveyed, it becomes necessary to con- 
sider tbe curvature of tbe eartb's surface; tbis brancb of 
surveying is called Geodesic surveying. 

2. Extensive geodesic operations prove tbat tbe eartb 
is an oblate spberoid, tbe sbortest diameter of wbicb coin- 
cides "witb tbe terrestrial axis, and all of wbose meridians, 
are equal ellipses. Tbe meridian lines, bowever, differ so 
little from tbe circumferenc* of circles, tbat tbey may be 
taken for tbem, except wben great accuracy is required. 
Tbe eartb, will, tberefore, in tbe following pages, be re- 
garded as a perfect spbere. 

8, Tbe operations necessary to tbe successful execution 
of a Geodesic Survey, require tbe minutest attention, and 
wben performed, numerous corrections are to be applied to 
tbe measured lines and angles, on account of tbe various 
causes of error incident to sucb operations. 

To investigate tbose causes of error, and to deduce rules 
for correcting tbe errors, in all cases, would far exceed 
tbe limits of an elementary treatise. We sball, tberefore, 
attempt notbing more tban a brief outHne of tbe operations 



SEC. L] TRIANGTJLATION. 173 

of a trigonometric survey, with, tlie application of some of 
the more important corrections. 

4. It may be observed tliat most of the operations de- 
scribed in this section, are equally applicable, whether we 
regard the area surveyed as plane or spherical : in either 
case, the basis of an accurate survey, is an extensive sys- 
tem of triangulation. 

6. After having made a preliminary examination or re- 
connaissance of the territory to be surveyed, suitable stations 
are selected at the most prominent points, and these points 
are marked by staves or signals. 

A hase line is then measured. The lengtb of the base 
will, in general, depend upon the magnitude of the survey, 
and each, extremity is marked by a signal. 

The next step is the triangulation. At each extremity 
of the base, the angles between the base, and the lines 
drawn to each of the visible signals, are carefully meas- 
ured by means of a theodolite. The sides of the triangles 
thus obtained, serve as nqw bases upon which, other trian- 
gles may be formed, and so on, until the entire area is 
covered by a net-work of triangles. 

6. This system of triangles is called the primary system, 
and the operation of forming them is called the primary 
triangulation. Within the primary triangles, and depending 
upon them, a system of smaller triangles is formed in the 
same manner, called the secondary system ; and if the extent 
or importance of the work should demand it, the secondary 
may be sub-divided into tertiary triangles. 

Having completed the triangulation, the characteristics 
, of the surface, such, as roads, streams, villages, boundaries, 
&c., are filled in by means of the compass, plain table, or 
some of the methods abeady explained. 

After the field work is completed, the triangles, when 
regarded as spherical, are reduced by applying the formula 
for spherical excess, hereafter explained, and other neces- 
sary corrections, and thus the whole work is plotted upon 
paper. 



174 ELEMENTS OF SURVEYIlfG. [BOOK IV. 

PRELIMIlSrARY EECONKOISSANCE AND ESTABLISHMENT OF 

SIGNALS. 

7. Before commencing a trigonometrical survey, an ex- 
amination of the entire territory should be made for the 
purpose of selecting a location for the base line, and proper 
points for stations ; this examination should be more or 
less elaborate, according to the nature and extent of the 
survey. 

The proper distribution and combination of the trian- 
gles, so as to adapt them to the survey in hand, require 
great judgment and care, and but few rules can be given for 
the selection of trigonometrical points. Those points should, 
in general, be chosen in such a manner, that they may be 
distinctly visible from each other, and so that the triangles 
formed, by uniting them, may be as nearly as possible 
equilateral. 

It is easily seen, that a triangle which has an obtuse 
or a very acute angle, will experience a greater change of 
form for a given error, than one which is nearly equilate- 
ral ; and since the accuracy of each triangle depends upon 
the preceding ones, it is further evident, that the introduc- 
tion of a single ill-conditioned triangle, might vitiate the 
whole survey. Except in extreme cases, no angle, less than 
80°, should be used, and even angles of 30° should not be 
admitted when the locality can be so chosen as to prevent 
it. The base is usually much shorter than the sides of the 
primary triangles ; these sides, however, should be increased 
as rapidly as is consistent with the above remarks. 

8. The accompanying diagram will illustrate the man- 
ner of increasing the sides without introducing ill-con- 
ditioned triangles. Having measured the base AB, and the 
requisite angles, the triangles ABG and ABD, may be de- 
termined, and the line i) (7 computed; with Z>(7 as a base, 
the triangles JDCU and BGF are formed, and thence JERF, 
and JSGF, in which the sides are much greater than the 
base AB. 






SEC. I.] SIGNALS. 175 



j)^ J— I s.'^c 



In tliis manner tlie sides may be increased to any de- 
sirable extent. An ordinary map of the country, or a 
sketch made witli tbe pocket compass, will be of material 
assistance in making a proper distribution of the stations. 

9. The stations are marked by signals, which may be 
constructed in a great variety of ways, depending upon the 
locality of the stations, and the lengths of the sides of the 
triangles. 

Sometimes a signal has to be raised above the level of 
the adjacent country, in which case it is constructed of 
timbers, and upon the apex, is placed a vertical staff, bear- 
ing a flag. The exact trigonometrical point is determined 
by a plumb-line, suspended from the apex of the signal. 

A temporary signal may be constructed with three or 
four pieces of scantling framed and traced, 
as shown in the annexed figure, with a short 
pole projecting from the apex. The plumb 
determines the point B, which is the exact trig- 
onometrical point over which the theodolite 
is to be placed. Where the sides of the trian- 
gles are not very great, a pole, planted ver- 
tically, and surmounted by a flag, will an- 
swer as a signal. 

In order to distinguish the different signals, the 
which they bear, should be different from each other. 
They may be formed by arranging stripes of white and 




176 ELEMEl^TS OF SURVEYING. [BOOK IV. 

red, according to some pre-arranged plan, and tlie flags of 
tlie different stations should be entered in a book. For 
tbe purpose of future reference, tbe trigonometrical point, 
at each station, as B, should be indicated by a permanent 
mark. If the point falls upon a rock, a hole may be drill- 
ed to show the locality; or if not, a mark-stone may be 
sunk under the point, deep enough to be beyond the reach 
of accident. A record of the monument should be pre- 
served, together with its reference to some of the perma- 
nent objects in the neighborhood. 

In order to render the signals visible from the distant 
stations, polished tin plates are sometimes attached to the 
signal-post, so as to reflect the sun towards the stations at 
certain hours of the day. The Drummond-light has also 
been used to show very distant stations. A light may also 
be produced that can be seen at a distance of 60 or 70 
miles, by placing a ball of lime about a quarter of an inch 
in diameter, in the focus of a parabolic reflector, and heat- 
ing it intensely by a stream of oxygen gas, directed by a 
blow-pipe, through a flame of alcohol. If obstacles, as trees, 
and under-brush intervene, vistas have to be opened along 
the lines, from station to station. 



MEASUEEMENT OF A BASE LINE. 

10. The measurement of a base line on which the ac- 
curacy of the entire survey depends, is one of the most 
difi&cult operations of geodesic surveying, and one, for the 
successful accomplishment of which, art and science have 
been strongly taxed. The selection of a proper site for a 
base line, forms one of the first objects of the prehminary 
reconnaissance. It should, if possible, be fixed on an open 
plain. It must be so chosen, that the surrounding signals 
may be distinctly seen from its extreme points ; and hence, 
those signals which mark points of the adjacent triangula- 
tion, should be selected with reference to the base. The 
length of the hase^ should, in a measure, depend upon the 
magnitude of the survey, though circumstances seldom 
admit its being taken more than 6 or 8 miles in length. 



SEC. I] BASE LINE. 177 

11. Different instruments iiave been used for measuring 
base lines, such, as steel chains, glass, platinum and deal 
rods ; and more recently, a combination of rods, of differ- 
ent metals, so adjusted, that the apparatus maintains an in- 
variable length at all temperatures. This last mentioned 
apparatus, has been much improved, and most successful!}^ 
used by Prof. Bache, in the Survey of the United States 
Coast. 

12. In minor surveys, where the base line does not 
much exceed 1000 or 2000 feet, sufficient accuracy may be 
attained by the use of wooden rods. To render the rods 
less susceptible of change, from moisture, they should be 
saturated with, boiling oil, and covered with, a thick coat- 
ing of varnish. 

The ends of the rods should be protected by metallic 
caps, which prevent their wearing, and insure a more per- 
fect contact. 

When the rods are prepared for use, they should be 
carefully compared with some standard measure, and from 
time to time this comparison should be repeated, in order 
to detect any minute change of length, should sucb change 
take place. 

13. The following method of measuring a base line of 
1000 or 2000 feet, may be rendered very accurate. 

Having decided upon the direction of the base, and 
measured it carefully, two or three times with a chain, let 
a theodolite be planted at one end of the line, and direct- 
ed upon a flag, planted at the other. Then, by means of 
the vertical limb, let a row of pickets be driven along the 
base, taking care to plant them at a distance from each 
other, equal to the length of one of the deal rods. Then, 
plant in the place of each picket, a vertical post, 6 or 8 
inches in diameter, and projecting a sufficient distance 
above the surface of the ground. If necessary, let the 
posts be steadied by heaping about them, earth or stones. 
Next, with the assistance of a spirit-level, let each post be 
sawed off, so as to bring their tops to the same horizontal 
12 



17i 



ELEMENTS OF SURVEYING. [BOOK IV. 



plane, and by means of the theodolite, let a line be marked 
on the top of each post, in the direction of the base. 
This line will determine the direction in which the rods 
are to be placed, and the contact of the ends must all be 
on this line. 

The contact of the rods should be made with great care, 
so as to avoid moving the rod already established ; and 
this will be more readily done, when three rods are used. 
The measurement should be repeated two or three times 
to guard against error, 

14. If the nature of the ground does not admit of the 
posts being brought to a level, let them, by means of the 
theodolite, be brought into an oblique plane AB, and after 

B 




having measured, as before, the line AB, determine accu- 
rately the difference of level between the points A and ^, 
equal to BG: then, from the right-angled triangle ABC, we 
should find the horizontal distance AC =^ V A^ — BC^. 

15. In very extensive surveys, the base should be several 
miles in length, and the apparatus for measurement, as well 
as the operations on the field, become more complicated. 
For a full description of a very perfect hase apparatus, and 
the method of using it, the reader is referred to Prof. 
Bache's pamphlet, on the subject — ^the details of the descrip- 
tion would exceed our limits. 



TRIANGULATION. / 

16. The theodolite is generally used for measuring the 
angles of a trigonometric survey. The extent of the survey,, 
and the standard of accuracy to which the results are re- 
quired to conform, must determine the size and perfection 
of the instrument to be employed. The angles of the pri- 
mary triangles of the United States Coast Survey, are meas- 
iired with theodolites, whose horizontal circles are 24 or 80 



SEC. L] 



TRIANGULATION. 



179 



inclies in diameter; and to eliminate as mucli as possible, 
every source of error, great numbers of operations are made 
on eacli station, tbe readings being made on different points 
of the arc. Usually from 40 to 60 observations are made 
for each angle — one measurement, with the telescope direct, 
and one with it reverted, constituting a complete observa- 
tion. With these precautions, it has been found that the 
error in a primary triangle (where the sum of its three an- 
gles has been compared with 180°), has fallen much with- 
in 3 seconds. The error of 3 seconds has been adopted as 
the highest admissible limit of error. 

17. Observations are also made at the principal stations 
upon the pole-star, and other stars near the pole, for the 
purpose of determining the angle, made by the sides of the 
triangle with the meridian. In minor surveys, and in a 
secondary triangulation, the operations are much less elabo- 
rate ; still, every precaution is to be taken to insure the 
greatest attainable accuracy. As a general rule, all the an- 
gles of every triangle, should be measured, if possible. 

18. To illustrate the manner of carrying on a minor 
triangulation, let us refer to the plan of the harbor [plate 
6], in which AB is the measured base, C, D, E, &c., tri- 
angulation points, at which signals have been erected. 
Commence the triangulation at A^ the west end of the 
base ; and for convenience in plotting, it would be well 
to make the line, passing through the point, and 180" 
parallel, in each position of the instrument, to the base 
AB. Having brought the of the vernier to the of the 
limb, clamp the vernier plate, and direct the upper teles- 
cope to the signal at B, and clamp the limb. Enter the 
observation as in the following table: 

OBSERVATION AT STATION A. 



Name of Station. 


Vernier I. 


Vernier II. 


Mean. 


Station B 


00° 00' 00" 


00' 00" 


00° 00' 00" 


Station E 


72° 24' 55" 


25' 5" 


72° 25' 00" 


Station G 


138° 34' 56" 


35' 4" 


138° 35' 00" 


&c. 


&c. 


&c. 


&c. 



180 ELEMENTS OF SirRYETIIfG. [BOOK IV. 

Having recorded tlie reading of tlie first vernier, and 
tlie minutes and seconds of the second vernier, unclamp 
tlie vernier plate, and direct tlie telescope to tlie station at 
E, and record both verniers, as before. Again unclamp the 
vernier plate, and direct the telescope on the signal at G; 
and then read and record, as before. 

Having determined the angles subtended by all the 
signals visible from J., let the theodolite be removed to 
B. Bring the of the vernier I to 180° on the limb, and 
direct the telescope on the signal at A — the line (0°, 180°) 
will then be parallel to its first position, and the limb may 
be clamped. Eead now the angles to the signals at J., E, 
(7, &c., and record as before. 

If the theodolite is now removed to the station E, the 
line (0°, 180°), may be made parallel to its first position, 
by adding 180° to the reading of the first vernier, from A 
to E^ and then directing the telescope on the signal at A. 
The line (0°, 180°), will thus be made parallel to AB, and 
the reading may be made and recorded as before ; and 
so on until all the stations have been visited, and the an- 
gles measured. From the field records, the angles BAE, 
EAO, ABEj EBG^ ko,.^ may be easily deduced, the whole 
may be plotted on paper, or the several sides may be com- 
puted trigonometrically. It may be observed that the line 
(0°, 180°), has been made parallel to the hase line at each 
station ; where great accuracy is required, this cannot be 
done, since a single reading is insufficient to give the angle. 
The angle is then determined, as directed in the previous 
article, or by means of the principle of repetition. 

19. To illustrate this principle of repetition, suppose the 
of the vernier to coincide with the of the limb, and the 
telescope to be directed, from the station ,4, upon one of the 
objects, as the signal at B. Clamp the limb, and unclamp- 
ing the vernier plate, direct the telescope on the second ob- 
ject, as the signal at E. If we now clamp the vernier 
plate, and unclamping the limb, direct the telescope on the 
signal at B, the line (0°, 180°), of the limb, will make 
with AB, an angle equal to BAE. Again clamp the limb, 



SEC. I.] 



TRIAITGULATION-. 



181 



and unclamping tlie vernier plate, direct tlie telescope on 
the signal at E. The reading will evidently be equal to 
twice the angle BAE^ and if we repeat the operation, the 
reading will be three times the angle, and so on. After 
ten repetitions, if we add 360° each time the of the 
vernier passes the of the limb, the final reading will be 
ten times the angle BAE^ affected with the joint errors of 
the ten observations, and one-tenth of this will be the read- 
ing required, to a greater degree of accuracy than could 
probably be attained by a single observation. 

20. The method of reading angles, by this mode, is as 
follows : 

Angles at station A, between signals B (left), and E 
<right.) 

June 8th^ 1851. 



No. of Eepe- 
titions. 


Vernier I. 


Vernier 
II. 


Mean of Verniers. 




1 


72° 24' 55" 


25' 5" 


72° 25' GO" 


2 


144° 49' 55" 


50' 0" 


144° 49' 58" 




3 


217° 14' 50" 


15' 10" 


217° 15' 00" 




4 


289° 39' 50" 


40' 00" 


289° 39' 55" 
Mean reading 


4)289° 39' 55" 






72° 24' 59" 



FILLmG UP THE SURVEY. 

21. After the triangulation is completed, the interior 
may be filled up by the aid of the Compass, or the plane- 
table. 

USE OF THE COMPASS. 



22. When the secondary and tertiary triangles have been 
considerably multiplied, the compass is taken in hand. 
The field-notes may be kept in the following manner. Di- 
vide a page of the note-book into two equal parts, by two 
parallel lines near to each other, and consider each part as 
a separate leaf or page. Each leaf is divided into three 



182 



ELEMENTS OF SURVEYING. [BOOK IV. 



spaces, and tlie middle space is generally smaller than either 
of tlie others, which are equal. 

The notes begin at the bottom of the first page, and 
run up the page to the top. They then commence again 
at the bottom of the next page, and run up to the top; 
thence to the bottom of the third page, and thus, for as 
many pages as the work may require. 

"When the compass is used in the way we are about to 
explain, the distances to objects which lie on the right or 
left of the courses, are determined by means of offsets. 

The beginning of every course is designated in the mid- 
dle column by 0, and the bearing is entered directly above. 
The other figures of the middle column, express the dis- 
tances from the beginning of each course to the offsets, and 
those in the side columns indicate the lengths of the offsets, 
or the distances to objects on the right or left of the com- 
pass lines. 

To explain more definitely the manner of using the 
compass on the field, let us suppose that we have deter- 
mined the prominent points and longer lines with the 
theodolite. Place the compass at A (Plate 6), and take the 
bearing of the line AU, which is S 12° W. 




Enter this bearing at A. Then measure along the line 



SEC. I.] THE PLANE-TABLE. 183 

AE any distance, as Aa equal to 130 yards, and make an 
oflFset to the lake, which we measure and find to be 50 
yards. Enter the 130 in the middle column, and as the 
lake lies on the right (in going from A to E\ we insert 
the 50 in the right hand column. 

We then measure along the line AE to h, 350 yards 
from A. Here we make a second offset to the lake, and 
find it to be equal to 100 yards. Having entered the dis- 
tances in the notes, we measure to g, the point where the line 
AE crosses the creek, and we enter the distance from J., 
415 yards. 

At c?, we lay off an offset on the left, to the pond, 70 
yards : at e, an offset to the mouth of the creek, 150 yards : 
and at E^ where the course terminates, an offset to the 
lake, of 160 yards. The entire distance from A io E \s, 
800 yards. 

At E^ we take the bearing to H^ which is N 50° E. 
Having measured along this line to / 315 yards, we make 
an oflfeet to the pond, on the left, of 50 yards, and to the 
shore, on the right, of 90 yards. Having entered these 
distances, we recommence the notes at 315 below, which we 
suppose to be at the bottom of the second page. Having 
reached H, the extremity of the course, we enter the en- 
tire distance from E^ 680 yards. "We next take the bear- 
ing to i^ S 52° E. We then measure the distances to m, 
n, jp, and I, and enter them, together with the offsets, as 
in the notes. 

23. It is also well to make, in the columns on the right 
and left, such sketches of the ground, fields, houses, creeks 
and rivers, as will afford the means of making an accu- 
rate delineation on paper. 

THE PLAKE-TABLE — ITS USES. 

24. PI. 3, Fig. 1. The plane-table consists of two parts ; 
a rectangular board CBBA, and a tripod ERG, to which 
it is firmly secured. 

Directly under the rectangular board are four milled 
screws which pass through sockets inserted in a horizontal 



184 ELEMENTS OF SURVEYING. [BOOK IV. 

brass plate : these screws are worked against a second lio- 
rizontal plate, for the purpose of levelling the table; the 
table having a ball and socket motion, similar to the limb 
of the theodolite. 

For the purpose of levelling the table, a small detached 
spirit-level is used. This level being placed over the 
centre, and also over two of the levelling screws, the screws 
are turned contrary ways until the level is horizontal; 
after which, it is placed over the other two screws, and 
made horizontal in the same manner. 

Between the upper horizontal plate and the table, there 
is a clamp-screw, similar to the clamp-screw of the theodo- 
lite, which being loosened, the table can be turned freely 
about its axis. There is, also, a small tangent-screw, by 
which the smaller motions of the table are regulated, after 
the clamp-screw is made fast. Neither of these screws can 
be seen in the figure. 

The upper side of the table is bordered by four brass 
plates, about one inch in width, and the centre of the table 
is marked by a small pin, F. About this centre, and tan- 
gent to the sides of the table, conceive a circle to be de- 
scribed. Suppose the circumference of the circle to be di- 
vided into degrees and parts of a degree, and radii to be 
drawn through the centre and the points of division. The 
points in which these radii intersect the outer edge of the 
brass border, are marked by lines on the brass plates, and 
the degrees are numbered in the direction from left to 
right, from the point L to the point ij 180°, and from the 
point / to the point i/, 180°. In some plane-tables, how- 
ever, they are numbered from to 360°. 

There are, generally, diagonal scales of equal parts cut 
on the plates DLG and AIB^ the use of which will be ex- 
plained hereafter. 

Near the two other edges of the table, two small grooves 
are made, into which the plates of brass BB and CA are 
fitted, and these plates are drawn to their places by means 
of milled screws, which pass through the table from the 
under side, and screw firmly into the plates. The heads 



SEC. I] THE PLANE-TABLE. 185 

of two of the screws, Q and S^ are seen in the figure, as 
also one of the plates and its two screAvs in Fig. 3. The 
object of these plates is to confine a sheet of paper on the 
table. By loosening the screws, and pressing them up- 
wards, the plates are raised above the surface of the table; 
the edges of the paper can then be placed under them : 
then, by turning the screws back again, the plates are 
drawn down and the paper held tightly. Fig. 1 represents 
the table with the paper partly put upon it : one edge of 
the paper has been placed under the plate DB^ and the 
screws S and Q, tightened. The paper, before being put 
on, should be moistened, in order to expand it ; and then, 
after it has been dried, it will fit closely to the table. 

A ruler, AB (Fig. 2), with open vertical sights, is used 
with the plane-table. This ruler has a fiducial edge, which 
is in the same vertical plane with the hairs of the sights. 
A ruler with a telescope, and a vertical limb, similar to the 
vertical limb of the theodolite, is sometimes used with the 
plane-table. A compass, also, is often attached to the table, 
to show the bearings of the lines. 

The plane-table is used for two distinct objects, 

1st. For the measurement of horizontal angles. 

2dly, For the determination of the shorter lines of a 
survey, both in extent and position. 

TO MEASURE A HORIZONTAL ANGLE. 

25. Place, by means of a plumb, the centre of the table 
directly over the angular point : then level the table ; after 
which, place the fiducial edge of the ruler against the small 
pin at the centre : direct the sights to one of the objects, 
and note the degrees on the brass plate ; then turn the 
ruler and sights to the other object, and note the degrees 
as before. If the ruler has not passed over the point, 
the difference of the readings is the angle sought ; but, if 
it has, the larger taken from 180°, and the remainder added 
to the smaller, gives the required angle. 

TO DETERMINE LINES IN EXTENT AND POSITION. 

26. Having placed a paper on the table, examine the 



186 ELEMENTS OF SURVEYING. [BOOK lY. 

objects and lines whicli are to be determined, and select 
for a base a convenient portion of sucIl a line of those 
already formed in the triangulation, that most of the ob- 
jects can be seen from its extremities. Then place the 
plane-table with its centre, nearly, though not accurately, 
over one extremity of the base ; make it truly horizontal, 
and turn it until the larger part of the paper lies on the 
same side of the base with the objects. 

Then, tighten the clamp-screw, and mark with a pin the 
point of the paper directly over the station, which point is 
determined most accurately by suspending a plumb from 
the lower side of the table. Press the pin firmly on this 
point, bring the fiducial edge of the ruler against it, and 
sight to the other extremity of the base line, and mark 
with the pin or pencil, the direction of the line on the 
paper. Sight in like manner to every other object, and 
draw on the paper the corresponding lines, numbering them 
from the base line, 1, 2, 3, 4, &c. 

Then, with a pair of dividers, take from the scale a 
certain number of equal parts to represent the base, and 
lay off the distance on the base line from the place of the 
pin. Take up the table, carry it to the other extremity 
of the base, and place the point of the paper correspond- 
ing to that extremity, directly over it. Place the fiducial 
edge of the ruler on the base line, and turn the table, by 
means of the tangent-screw, until the sights are directed to 
the first station. If, however, in bringing the table to this 
position, the corresponding point of the paper has been 
moved from over the extremity of the base line, move the 
legs of the tripod until it is brought back to its place. 
Let the table be then levelled, after which, place the ruler 
again on the base line, and bring the table to its proper 
position by the tangent-screw, and continue the adjustment 
until the extremity of the base line on the paper is directly 
over the station, and in the same vertical plane with the 
base line on the ground. Then direct the sights to all the 
objects sighted to from the other station, and mark the 
lines 1, 2, 3, 4, &c., from the base line, as before. The 
intersections of the corresponding lines 1,1, 2,2, 3,3, 4,4, 



SEC. I.] 



THE PLANE-TABLE. 



187 




&c,, determine, on the paper, the positions of the several 
objects ; and a reference of these lines to the scale of equal 
parts, determines the true distances. 

27. Let it be required, for 
example, to determine, by 
means of the plane-table, the 
relative positions of several 
houses. 

From station J., and on 
one of the lines of the tri- 
angulation, as AB^ measure 
the base line AJSf, which we will suppose equal to 300 
yards. Place the plain-table at A, and sight to the corners 
of the houses, and mark the lines 1, 2, 3, 4, &c. Then 
remove the table to N, and sight to the same corners as be- 
fore, and draw the lines as in the figure. The points at 
which they intersect the corresponding lines before drawn, 
determine the corners of the houses. The front lines of 
the houses may then be drawn on the paper. Draw lines 
at right angles to the front lines, and on them lay off the 
depths of the houses, with the same scale as that used for 
the base line. 

To find the length of any line drawn on the paper, as 
the line 1, drawn through A, for example, place the divi- 
ders at A and extend them to the other extremity of the 
line, and then apply the line to the scale. The length of 
the hue 1 is equal to 198 yards. 



28. In this example, we de- 
termine from the base line 
CZ), the positions of the points 
F, E, and H. 




OF CHANGING- THE PAPER. 

29. When one paper is filled, and there is yet more 
work to be done, let the paper be removed, and a second 
paper put on the table ; after which, the table may be 
used as before. 



188 ELEMENTS OF SURVEYING. [BOOK IV. 

Now, in order tliat tlie two papers may be put toge- 
ther and form one entire plan, it is necessary that two 
points determined on the first paper, be also determined 
on the second; and then, by placing the lines joining 
these ppints, one on the other, all the lines on the two 
papers will have the same relative position as the corres- 
ponding lines on the ground ; and the same for as many 
papers as it may be necessary to use. If different scales 
are used, the corresponding points will not join, and then 
the work must be reduced to the same scale, before the 
papers can be put together. 

In the first example, the position of the point F was de- 
termined, in order to unite the first paper with the second. 

In the second example, we sighted from G and D, the 
extremities of the base line, to the points N and F] we 
thus determined the line NF on the second paper. Pla- 
cing the line NF of the one paper on NF of the other, we 
have the following plan. 



Er^ TvH" 



\ 




In this plan, all the points and lines are accurately laid 
down. Any number of papers may be joined in the same 
manner. 

80. The principal use of the plane-table is for the in- 
terior filling up of trigonometrical surveys; it is also used 
with advantage, when only a plot of a field is wanted. 

It ought not be used for the determination of long lines, 
nor can it be relied on for determining • extended areas. 

Having finished the field-work, some corrections are ne- 
cessary, before plotting the survey. The principal correc- 
tions are, the reduction to the centre of the station, and 
the correction for spherical excess. 



SEC. L] 



CORRECTIONS. 



189 



REDUCTION TO THE CENTRE. 

31. It sometimes happens tliat fixed objects, as steeples, 
towers, and tlie like, are used instead of signals, in a sur- 
vey. The theodolite cannot be placed over the centre of 
such stations. In all such cases, the instrument must be 
planted as near as possible to the station; then the angles, 
subtended bj the various objects being measured, the true 
angle subtended at the centre of the station, is computed 
by the following formula. -^ B 



Suppose A^ B and (7, to be 
the three stations. Let us sup- 
pose that the theodolite cannot 
be placed over (7, but that it 
can be placed at i), a point 
near G. 



Let the angles ABB and 
ABG be measured ; also the 
distance CB. The true angle 
AGB may then be found. 




C D 



For, AEB = AGB+ GAB (Geom., Bk. L, Prop. 25, C. 6); 

and AEB = ABB + BBG: 

hence, by equating the equal values, 

AGB+ GAB = ABB + BBG, 

AGB= ABB + BBG - GAB. 

GB : : sin BBG : sin BBG', 

GB 

BG 

sin ABG 

GB 
sin GAB = 



or, 
But, 



and 



BG 



AG 



sin BBG 
: GB :: 



sin BBG: 



sin GAB: 



AG 



sin ABG. 



Hence, by substitution, we have 
GB 



I GB GB \ 

AGB = ABB + ^ ^ sin BBG- j^ sin ABG) ; 

and since the point B is very near G, as compared with 
the distances BG and AG, those distances may be comput- 
ed with the measured angle ABB. 



190 ELEMENTS OF SURVEYING. [BOOK IV. 

It is to be observed, that when tbe radius is unity, in 
tbe above formula, the natural sines of the angles are used, 
and that the correction within the parenthesis, is expressed 
in linear units, and will be positive or negative, according 
as the second term is less or greater than the first. 

To convert the linear correction into seconds of an arc, 
whose radius is unity, let the deduced correction, within 
the parenthesis, be denoted by c. Then, since the radius 
is 1, we shall have 

length of semi-circumference. 
: the linear correction. 
: : the number of seconds in 180°. 
: the number of seconds in the correction : 
that is, denoting the number of seconds in the correction 
by n, 

3.1416 : c : : 648000" : n ; or w = c X 206264.3" : 
c will, in all cases, be a very small fraction. 

This correction is not often necessary, for in extensive 
operations, such stations are chosen as will allow of the 
measurement of all the angles, and in secondary triangles, it 
is admissible to measure only two of the angles. 

SPHERICAL EXCESS. 

32. It has already been noticed, that the triangles meas- 
ured, are on the surface of a sphere, and consequently, the 
angles taken between any three points, by a theodolite, are, 
strictly speaking, the angles of a spherical triangle ; hence, 
the sum must exceed 180°, (Geom., Bk. IX., P. 14). This ex- 
cess is called the spherical excess. In the processes of trian- 
gulation, we reduce all triangles to rectilineal triangles ; and 
hence, the sides of the triangle, which we seek, are chords 
of the sphere, and not arcs measured on the surface. 

33. In small triangles, where the sides do not exceed 
6 or 8 miles, the spherical excess may be altogether ne- 
glected; but in large triangles, it must be taken into ac- 
count. Of all the methods, yet known, of correcting for 
the spherical excess, Legendre's is considered the best. 



SEC. 1] SPHERICAL EXCESS. 191 

This metliod is based upon the proposition that, the area 
of a spherical triangle, whose sides are very small when com- 
pared with the entire surface of the sphere^ is nearly identical 
ivith a rectilineal triangle^ whose sides are of the same length 
as those of the spherical triangle^ and whose angles are each 
dimhiished hy one-third of the spherical excess. 

34. The first thing, then, is to find the spherical ex- 
cess, and for this, we must know the area of the triangle. 
The rules for determining the area of the rectilineal trian- 
gles, will afford results sufiicientlv near, and the first ap- 
proximate area may be computed in square feet, as though 
the triangle were rectilineal. Having found this area, the 
formula of Legendre, gives the logarithm of the spherical 
excess, estimated in seconds, equal to the logarithm of the 
area of the triangle computed in square feet, minus the 
constant logarithm 9.326770. That is, if we put 

E = the spherical excess, in seconds. 
A = area of the triangle, in square feet. 
Constant log. = 9.326770 ; 
we shall have. 

Log ^= log ^-9.326770. 

Having found the spherical excess, we divide it by 3, 
and then diminish each angle of the triangle by the quo- 
tient ; the sum of the three angles should then be equal to 
180°. With these new angles, we compute all the parts of 
the triangle. 

35. The spherical excess between latitude 25° and 45°, 
is about 1" for an area of 75.5 miles ; hence, to obtain a 
close approximation to the spherical excess, divide the num- 
ber of square miles in the area of the triangle hy 75.5, the 
quotient will be the number of seconds required. 

36. To find the spherical excess, knowing the two sides 
a and 6, and the included angle G. 

a h sin G. 

area= — — . 

2 R 



192 ELEMENTS OF SUllVEYI^fG. 



[BOOK IV. 



Suppose a = 248230 feet, b = 212628 feet, and 0= 103° 
19' 10". 

a 248230 log 5.394854 i 

h 212628 log 5.327620 

C. . 103° 19' 10" . . . log sine . . . 9.988158 



r „. 2 ar. comp. diminished by 10 . . 1.698970 



Log of the area. 
Loff of E 



Constant logarithm 



20.409602 
10. 

10.409602 
9.326770 



= log A 



Hence, JE= 12.1" 1.082832. The sum of 

the three measured angles ought therefore to exceed 180°, 
by this amount. The angles being corrected, by subtract- 
ing 4.3-" from each, the parts of the triangle may be com- 
puted, by regarding the sides as rectilineal. 

PLOTTING- THE TEIANGULATIOIST. 

87. The sides of the triangles being computed, after 
having made the necessary corrections, the work may then 
be plotted, as already explained, either by means of the 
circular protractor, or by the method of chords. 

THE CIRCULAR PROTRACTOR. 

38. This instrument consists of a brass circular limb 
(PI. 2, Fig. 4), of about six inches in diameter, with a 
movable index AB, having a vernier at one extremity A, 
and a milled screw at the other extremity B, with a con- 
cealed cog-wheel that works with the cogs of the limb, and 
thus moves the index AB about the centre of the pro- 
tractor. At the centre of the protractor is a small circular 
glass plate, on which two lines are cut ; the point of their 
intersection, is the exact centre of the instrument. The 
limb is generally divided to half degrees ; the degrees are 
numbered from to 860. 

At the point, and at the opposite extremities of the 
diameter passing through that point, are small lines on the 
inner edge of the limb; the two extremities of the diam- 



SEC. 1] OF PLOTTING. 193 

eter, perpendicular to this latter, are designated in tlie same 
way. 

Two angular pieces of brass, eacli having a small and 
sharp steel pin at its extremity, are fastened to the index, 
and revolve freely around the lines ah and cd. The small 
screws, a, 5, c, and c?, move them in the directions of the 
lines a6, cd^ for the purpose of bringing the steel pins ex- 
actly into the line which passes through the . of the in- 
dex and the centre of the protractor. 

To adjust them to their places, place the centre of the 
protractor over a marked point, and the of the index to 
the of the limb. Then mark the place of the index by 
the pins: after which, turn the index 180°, and see if the 
pins will mark the same points as before. If they do, the 
index is adjusted ; if they do not, correct the error with the 
screws a, Z>, c, and d. 

TO LAY OFF AN ANGLE WITH THE PEOTRACTOR. 

39. Let its centre be placed over the angular point, and 
the diameter passing through and 180°, on the given line. 
Turn the screw that works the index, until the of the 
vernier, coincides with the division corresponding to the 
given angle; then let the angular brass pieces be turned 
down; the points dotted by the steel pins will show the 
direction of the required line. 

If this line does not pass through the angular point, 
the pins are out of place, and must be adjusted. 

FIRST METHOD OF PLOTTING. 

40. Suppose it were required to make the plan of the 
harbor on a scale of 450 yards to an inch. 

Divide the length of the base line AB^ which we will 
suppose equal to 1140 yards, by 450, and the quotient 2.53 
will express the length which is to represent the base line 
on the paper (Bk. I., Art. 54.) 

Draw an indefinite line AB, to represent the base, and 
having chosen any point, as A, for the first station, lay off 
2.53 inches to JB. The other extremity of the base line 
will thus be determined. 
13 



194 ELEMENTS OF SURVEYING. [BOOK lY. 

Then, place tlie circular protractor at A, and lay off 
tlie angle BAJS, and then the angle UAG. . Next, place 
the protractor at B, and lay off the angles ABE and EBO. 
The intersection of the lines AE and BE will determine 
the station E. Let the protractor be then placed at this 
point, and all the angles of station E, laid down. 

The point G, where EG intersects AG, and the point 
0, where EC intersects BO, will then be found. 

By placing the protractor at G and G, we can deter- 
mine the points I) and E, when the place, on the paper, of 
all the stations will be known. 

To unite the work done with the compass, spread the 
compass-notes before you, and draw through A a line to 
represent the meridian. This line makes an angle of 12° 
with the course AE. 

Then, lay off from the scale the distances Aa, Ab, Aq, 
Ac, Ad, Ae, and at the several points erect perpendiculars 
to AE. Lay off on these perpendiculars the lengths of the 
offsets, and the curve traced through the points so deter- 
mined, will be the margin of the lake. 

At E, draw a parallel to the meridian through A, and 
lay down the course Eff, which makes an angle of 50° with 
the meridian. Then, lay down the several distances to the 
offsets, and draw the offsets and lay off their lengths. Do 
the same for the course HI, and all the compass-work will 
be plotted. 

The work done with the plane-table (Art. 28), is united 
to the work done with the theodolite, by simply placing 
the line AN on the paper of the plain-table, upon the line 
AN", drawn on the plot of the triangulation. 

SECOND METHOD OF PLOTTING. 

41. Place the centre of the protractor near the centre 
of the paper, and draw a line through the points and 
180°. This line will have the same position with the cir- 
cular protractor that the base line AB had with the limb 
of the theodolite. 



SEC. I] METHOD OF CHORDS. 195 

Lay off then from the point an arc equal to the direc- 
tion from A to JS, also an arc equal to the direction AG, 
and through the centre point, and the points so determined, 
draw lines. Lay off in succession, in a similar manner, 
the directions taken at all the stations ; and through the 
centre point, and the points so determined, draw lines, and 
designate each by the letters of the direction to which it 
corresponds. 

Now, since all the lines drawn on the paper have the same 
position with the circular protractor, as the corresponding 
lines on the ground have with the limb of the theodolite, 
it follows that each direction wiU be parallel to its corres- 
ponding line upon the ground. 

Hence, any line may be drawn parallel to that passing 
through and 180°, to represent the base line AB. Having 
drawn such a line, and marked a point for the station A, 
lay off the length of the base, and the extremity will be 
the station B. 

Through A and B, so determined, draw parallels re- 
spectively to the lines corresponding to the directions A^ 
and BE, and the point of intersection will determine station 
K Through B and U draw parallels to the lines which 
correspond to the directions BO, GE, and their point of 
intersection will determine station C. Through G and E 
draw lines parallel to the lines corresponding to the direc- 
tions GE and ED, and the point of intersection will de- 
termine D. In a similar manner we may determine the 
stations F and G. 

METHOD OP CHORDS. 

42. Let us first prove that the chord of a given arc is 
equal io the sine of half the arc loith double the raditts. 

Let BAF be any given angle, 
and AR a line bisecting it. Let '^Sh^ 3<<^ '' 

DC he the chord of the arc GD, X%^ — ''X^' 

described with a given radius, ji:^^^^^'^^\ X_ 

and HF parallel to GD, the sine A Q F 

of half the given angle, to a radius AF== 2 AG. 



196 ELEMENTS OF SURYETIlfG. [BOOK lY. 

Since AF=2AC we have, from similar triangles, HF= 
2KG, but DC= 2KG, hence HF= CD. 

TO LAY OFF AN ANGLE. 

48. To avoid, as far as possible, / 
the use of fractions, let us suppose )^^ ^-^-X^ 
the radius of the table of natural /"'■'O'^r'''^^ \'^ 
sines to be 1 ten^ or 10 inches. .^^^^"^^ \ \;_ 

Take from a scale 5 equal parts, 
with which as a radius, from the centre J., describe an 
arc CD. Take from the table the natural sine of half 
the arc, and remove the decimal point one place to the 
left; the residt will express the sine of the arc to the 
radius 10, or the chord of half the arc to the radius 5. 
From the same scale, take this sine in the dividers, and 
from C, as a centre, describe an arc cutting CD in D ; 
draw AD, and CAD will be the angle required. 

This is the most accurate of all the methods of laying 
off an angle, and it may also be applied advantageously to 
the second method of plotting, thus : 

Draw a fine straight line, generally 
in the direction of the meridian or of 
the base line of the survey ; and also 
a line exactly perpendicular to it. From 
the point of intersection, as a centre, 
with a radius of 5 equal parts of the 
scale, describe the circumference of a 
circle cutting the straight lines in the points marked 
and 90°. 

To lay off an angle, as for instance, the angle 14° 29'. 
The half of it is 7° 14' 30", the natural sine of which is 
0.126005, or 1.26 to the radius of 10 inches. Set off from 
to &, as in the figure, this distance taken from the scale, 
and through the two points &, 5, thus determined, draw a 
straight line. This line should pass through the centre, 
and will make with the line (0, 0) the angle 14° 29' ; and 
any line on the paper drawn parallel to it, will make with 
the line (0, 0) the same angle. The further application is 
obvious. 




SEC. II.] MARITIME SURVEYING. 197 



SECTION II. 

MARITIME SURVEYIlSra. 

44. When, in connection with a trigonometrical survey 
on shore, a harbor is to be surveyed for the purpose of 
ascertaining the channels, their depth and width, the posi- 
tions of shoals, and the depth of water thereon, other 
means must be used, and other examinations made in ad- 
dition to those already referred to. 

Let buoys be anchored on the principal shoals and along 
the edges of the channel, and using any one of the lines 
already determined as a base, let the angles subtended by 
lines drawn from its extremities, to the buoys respectively, 
be measured with the theodolite. Then, there will be 
known in each triangle the base and angles at the base, 
from which the distances to the buoys are easily found ; 
and hence, their positions become known. 

Having made the soundings, and ascertained the exact 
depth of the water at each of the buoys, several points of 
the harbor are established, at which the precise depth of 
the water is known ; and by increasing the number of the 
buoys, the depth of the water can be found at as many 
points as may be deemed necessary. 

45. If a person with a theodolite, or with any other in- 
strument adapted to the measurement of horizontal angles, 
be stationed at each extremity of the base line, it will not 
be necessary to establish buoys. A boat, provided with 
an anchor, a sounding line, and a signal flag, has only to 
throw its anchor, hoist its signal flag, and make the sound- 
ing, while the persons at the extremities of the base line 
measure the angles ; — ^from these data, the precise place of 
the boat can be determined. 

46. There is another method of determining the places 
at which the soundings are made, that admits of great 



19'8 ELEMENTS OF SURVEYING. [BOO'E: IV. 

despatch, and wliidi. if the observations are made with- 
care, affords results sufl&ciently accurate. 

Having established, trigonometrically, three points which 
can be seen from all parts of the harbor, and having pro- 
vided a sextant, let the sounding be made at any place in 
the harbor, and at the same time the three angles subtend- 
ed by lines drawn to the three fixed points, measured with 
the sextant. 

The problem, to find, from these data, the place of the 
boat at the time of the sounding, is the same as example 
6, page 62. 

It is only necessary to measure two of the angles, but 
it is safest to measure the third also, as it affords a veri- 
fication of the work. 

The great rapidity with which angles can be measured 
with the sextant, by one skilled in its use, renders this a 
most expeditious method of sounding and surveying a 
harbor. 

The sextant is not described, nor are its uses explained 
in these Elements, because its construction combines many 
philosophical principles, with which the Surveyor cannot 
be supposed conversant. 



47. There is yet another method of finding the sound- 
ings, which, although not as accurate as those already ex- 
plained, will, nevertheless, afford results approximating 
nearly to the truth. It is this ; — ^Let a boat be rowed uni- 
formly across the harbor, from one extremity to the other 
of any of the lines determined trigonometrically. Let 
soundings be made continually, and let the precise time of 
making each be carefully noted. Then, knowing the 
length of the entire line, the time spent in passing over it, 
as also the time of making each of the soundings, we can 
easily find the points of the line at which the several 
soundings were made ; and hence, the depth of water at 
those points becomes known. 

48. If a person stationed on shore with a theodolite, takes 
the bearing of the boat, at every second or third sounding, 
determined by hoisting a flag, it will fix the positions of the 




SFC. II.]" MARITIME SURVEYING. 199 

soundings witli great accuracy. Soundings may thus be 
made along any number of known lines, and a comparison 
of the depths found on different lines, at or near their 
points of intersection, will show with what degree of ac- 
curacy the work has been done. 

Sounding-lines should be made of strong cord, and di- 
vided into feet or fathoms, by different colored rags or 
other marks. The lead is shaped like 
the frustum of a cone, with the base 
J5, hollowed out, to hold some grease. 
The land or mud of the bottom adheres 
to the grease, and thus shows the na- 
ture of the bottom, which should be en- 
tered in the field-book, and laid down 
upon the map. As the cord is liable 
to change its length, it should be com- 
pared from time to time with some 
standard. In tide-waters, the exact time 
of each sounding is to be noticed, and 
an assistant should note the height of the tide at regular in- 
tervals, upon a tide-guage. The tide-guage is permanently 
placed at some convenient point of the harbor, and its 
point is referred by means of a spirit-level, to some fixed 
bench-mark, on a level with mean low-water mark, to 
which all the soundings must be reduced. 

49. Having plotted the work done with the theodolite, 
as also the outline of the harbor traced with the compass, 
it remains to delineate the bottom of the harbor ; and this 
is done by means of horizontal curves, which have already 
been used to represent broken or undulating ground. 

Let the plane of reference be taken through low-water 
mark, or to coincide with the surface of the water at low 
tide. The accuracy with which the bottom of the harbor 
is to be delineated, will guide us in fixing the distance be- 
tween the horizontal planes of section. 

The first horizontal plane should be passed at a dis- 
tance below the shallowest point that has been sounded, 
equal to the number of feet fixed upon for the distance 
between the planes of section; and the curve, in which it 



200 ELEMENTS OF SURVEYIITa. [BOOK lY. 

intersects tlie bottom of tlie harbor determined as in Book 
in. Sec, II. And similarly, for the other horizontal planes 
of section. 

Having thus delineated the bottom of the harbor, and 
noted on the map the distance of each intersecting plane 
below the plane of reference, let such lines be drawn as 
will indicate the channels, shoals, sunken rocks, and direc- 
tion of the current. 

In the example given in plate 6, soundings have been 
made in three directions from the sand-bar in the harbor, 
and also from the rocky shore across to the light-house.. 



BOOK V. 

OF NAYIGATION. 



SECTION I. 

DEFINITIONS. 



1. "We have given, in tlie preceding parts of this -work, 
various applications of Plane Trigonometry. We propose, 
in this Book to explain the best methods of determining 
the place of a ship at sea. This application of Trigonom- 
etry constitutes the science and art of Navigation. 

2. There are two methods of determining the place of 
a ship at sea. 

1st. When a ship departs on her voyage, if we note 
her courses and the distance sailed, we may, at any time, 
by means of Plane Trigonometry, determine her place, very 
nearly. 

2d. By means of observations on the heavenly bodies, 
and the aid of Spherical Trigonometry, we may determine 
with great accuracy, the place of the ship. This method 
is called Nautical Astronomy. 

The first part of Navigation, viz., the cases which can 
be solved without the aid of observations on the heavenly 
bodies, wiU be alone treated of. 

8. The earth is nearly spherical. For the purposes of 
Navigation it may be considered as perfectly so. It re- 
volves round one of its diameters, called the axis, in about 
twenty-four hours. 

4. The great circle, whose poles are the extremities of 
the axis, is called the equator. The poles of the equator 



202 ELEMENTS OF SURVEYING. [BOOK V. 

are called the poles of the earth — one is called the north 
pole, and the other the south pole. 

5. The circumference of every great circle which passes 
through the poles, cuts the equator at right angles, and is 
a meridian circle. Every place on the surface of the earth 
has its own meridian ; but for the purposes of Geography 
and Navigation, all the meridians are reckoned from a par- 
ticular meridian, which is called the first meridian. The 
English have fixed on the meridian of the Greenwich Ob- 
servatory, for the first meridian. 

6. The longitude of any place is the arc of the equator, 
intercepted between the meridian of that place and the first 
meridian, and is east or west, according as the place lies 
east or west of the first meridian. 

7. The difference of longitude of two places is the arc of 
the equator included between their meridians ; this arc is 
equal to the difference of longitudes when they are of the 
same name, and to the sum of the longitudes, when they 
are of different names.' 

8. The latitude of a place is its distance from the equator, 
measured on the meridian of the place, and is north or south 
according as the place lies north or south of the equator. 

9. The small circles drawn parallel to the equator, are 
called parallels of latitude. The arc of any meridian inter- 
cepted between the parallels passing through any two 
places, measures the difference of latitude of those places; 
this difference is found by subtracting the less latitude from 
the greater, when the latitudes are of the same name, and 
by adding them when they are of different names. 

10. The sensible horizon of any place is an imaginary 
plane, supposed to touch the earth at that place, and to be 
extended indefinitely. 

A plane passing through the centre of the earth, and 
parallel to the sensible horizon, is called the rational horizon. 

The north and south line, is the intersection of the 
plane of the meridian circle with the sensible horizon, and 
the line which is drawn perpendicular to this, is called the 
east and west line. 



SEC. 1] 



NAVIGATION. 



203 



11. The course of a ship, at any point, is the angle which 
her track or keel makes with the meridian. So long as the 
course is unchanged, the ship would sail in a straight line, 
if the meridians were truly parallel ; but as the meridians 
bend constantly toward the pole, the direction of her path is 
continually changing, and she moves in a curve called the 
rhumb line. The course of a ship is indicated by the mari- 
ner's compass. 

12. The marin- 
er's compass consists 
of a circular card, 
whose circumfer- 
ence is divided into 
thirty-two equal 
parts called points ; 
each point being 
subdivided into four 
parts, called quar- 
ter points. 

To the under 
side of this card a 
slender bar of mag- 
netized steel, called 
a needle, is permanently attached. The direction of the 
needle corresponds to the diameter NS. The diameter EW, 
at right angles to NS, is intended to indicate the east and 
west points. The points of the compass are thus read : be- 
ginning at the north point, and going east, we say, north 
and hy east, north north east, north east and by north, 
north east; and so on, round the compass, as indicated by 
the letters. 

The card being permitted to turn freely on the pin, on 
which it is poised, as a centre, the line NS will always 
indicate the true magnetic meridian, but this, as we have 
seen in (Bk. II., Sec. 7-14), is not the true meridian, and 
hence, the variation must always be allowed for. 

On the interior of the compass box, in which the card 
swings, are two marks a and b, which lie in a line passing 
through the centre of the card, and the compass box is so 




204 ELEMENTS OF SURVEYING. [BOOK V. 

placed tliat this line sliall be parallel to tlie keel of tlie 
ship. Consequently, if & be placed towards tbe bow of the 
vessel, the point which it marks on the card will show the 
compass course, for the line NS is always on the magnetic 
meridian, and EW" is east and west. The course is gene- 
rally read to quarter points, and as a quadrant contains 
eight points, each point is equal to 90° -r- 8 = 11° 15' ; and 
a quarter point = 11° 15'H-4=2° 48' 45". The table of 
Khumbs, after the Traverse Table, shows the degrees in 
each course, to quarter points. 

13. A ship's rate of sailing is determined by means of 
an instrument, called the %, and an attached line called 
the log line. The log is a piece of wood in the form of a 
sector of a circle, the rim of which is loaded with lead, so 
that when it is heaved into the sea it assumes a vertical 
position. The log line is so attached as to hold the log 
square against the water, that it may not be drawn along 
after the ship as the line unwinds from the reel, by the 
ship's forward motion. 

The time in which the log line unwinds from the reel, 
is noted by a sand-glass, through which the sand passes in 
half a minute ; that is, in the one hundred and twentieth part 
of an hour. 

For convenience, the log line is divided into equal parts, 
marked by knots, and each part is equal to the one hun- 
dred and twentieth part of a nautical or geographical 
mile*. 

Now, since half a minute is the one hundred and twen- 
tieth part of an hour, and each knot indicates the one hun- 
dred and twentieth part of a mile, it follows that the mem- 
ber of knots reeled off while the half minute glass runs out, 
wiU indicate the rate of the ship's sailing per hour. 



* A geograpliical mile is one minute, or one-sixtieth of a degree, measured on 
tlie equator. Taking the diameter at 7916 English miles, the geographical mile 
will be about 6079 feet ; that is, one-sixth greater than the English mile, which 
is 6280 feet. 



SEC, II.] 



PLANE SAILING. 



205 



SECTION II. 



OF PLANE SAILING. 




14. Let tlie diagram 
EPQ represent a por- 
tion of the eartli's sur- 
face, P the pole, and 
EQ the equator. Let 
AB be an J rhumb line, 
or track described by 
a ship in sailing from 
A to B. 

Conceive the path of the ship to be divided into very 
small parts, and through the points of division draw meri- 
dians, and also the parallels of latitude 1% c'c, d'd, e'e, and 
B'B: a series of triangles will thus be formed, but so small 
that each may be considered as a plane triangle. 

In these triangles, the sum of the bases 
Ah' + he' + cd' -f de' + e/= AB', 
which is equal to the difference of latitude between the 
points A and B. Also, 

h'h + c'c + d'd + e'e +fB = BB', 
which is equal to the distance that the ship has departed 
from the meridian AB'P, and is called the departure in 
sailing from A to B. 

Therefore, the distance sailed, the dif- 
ference of latitude made, and the departure, 
may be represented by the hypothenuse, 
the base and perpendicular of a right- 
angled triangle, of which the angle op- 
posite the departure is the course. 

When any of the four parts above- 
named are given, the other two can be 
determined. This method of determining 
the place of a ship reduces all the elements to the parts 
of a plane triangle, and hence is called plane 




206 



ELEMEN"TS OF SURVEYIITG. [BOOK V. 



EXAMPLES. 

1. A ship from latitude 47° 30' N. has sailed S. W. by 
S. 98 miles. What latitude is she in, and what departure 
has she made ? 

Let G be the place sailed from, CB 
the meridian, and BOA the course, which 
we find from the table of rhumbs to be 
equal to 33° 45' ; then A will be the dis- 
tance sailed, equal to 98 miles. Also, AB 
will be the departure, and CB the differ- 
ence of latitude. 

Then by the formulas for the solution 
of right angled triangles, A 




As radius ar. c. 
: cos G 33° 45' 
: : AG 98 



0.000000 
9.919846 
1.991226 



GB 



81.48 



1.911072 



As radius ar. c. 0.000000 
: sin G 33° 45' 9.744739 
:: GA 98 1.991226 



AB 54.45 



1.735965 



Latitude left 47° 30' N. 

Dif lat. = 81.48 miles = 81.48 minutes = 1° 22' S. 



In latitude 



46° 08' 



Departure, 54.45 miles. 

2. A ship sails 24 hours on a direct course, from lat- 
itude 38° 32' N. till she arrives at latitude 36° 56' K 
The course is between S. and E. and the rate 5^ miles an 
hour. Required the course, distance, and departure. 

Lat. left 38° 32' K 24 X 5i = 132 miles = distance. 

In lat. 36° 56' 



Diflf. 1° 36' = 96 miles. 



As dist. 132 ar. c. 7.879426 
: diff. lat. 96 1.982271 

: : radius 10.000000 



: cos course 43" 20' 9.861697 



As radius ar. c. 0.000000 
: dist. 132 2.120574 

: : sin course 43° 20' 9.836477 



dep. 



90.58 1.957051 



SEC. Ill] TRAVERSE SAILING. 207 

Hence, tlie course is S. 43° 20' E,, and the departure 
90.58 miles east. 

3. A ship sails from latitude 3° 52' S. to latitude 4° 30' 
N,, the course being N. "W. by W. ^W. : required the dist- 
ance and departure. 

Ans. Dist. 1066 miles; dep. 939.2 miles W. 

4. Two points are under the same meridian, one in lat- 
itude 52° 30' K, the other in latitude 47° 10'/ N. A ship 
from the southern place sails due east, at the rate of 9 
miles an hour, and two days after meets a sloop that had 
sailed from the other : required the sloop's direct course, and 
distance run. 

Ans. Course S. 53° 28' E.; dist. 537.6 miles. 

5. If a ship from latitude 48° 27' S., sail S. W. by W. 
7 miles an hour, in what time will she reach the parallel 
of 50° south ? Ans. 23.914 hours. 



SECTION III 



OF TRAVERSE SAILING. 



15. When a ship, in going from one place to another, 
sails on different courses, it is called Traverse Sailing. The 
determination of the distance and course, from the place of 
departure to the place of termination, is called compounding 
or loorking the traverse. This is done by the aid of the 
*' Traverse Table," which has already been explained, and 
the method of working the traverse, is in all respects simi- 
lar to that adopted in the Prob. of Art. 34, page 123. 

EXAMPLES. 

1. A ship from Cape Clear, in lat. 51° 25' N"., sails, 1st, 
S. S. E. i E. 16 miles ; 2d, E. S. E. 23 miles ; 3d. S. W. 
by W. i W. 36 miles ; 4th, W. f K 12 miles ; 5th, S. E. 
by E. \ E. 41 miles : required the distance run, the direct 
course, and the latitude. 



208 



ELEMENTS OF SURVEYING. [BOOK V. 



We first form tbe table 
below, in wbicli we enter 
tlie courses, from tbe table 
of rhumbs, omitting the 
seconds, and tben enter 
tbe latitudes and depart- 
ures, taken from tlie tra- 
verse table, to tbe nearest 
quarter degree. Thus, in 
taking tbe latitude and 
departure for 25° 18' we 
take for 25^°. The dif- 
ference of latitudes gives 
tbe line AG, and tlie dif- 
ference of departures the 
line GF. 




TEAVERSE TABLE. 



Courses. 


Dist's. 


Diflf. of Latitude. 


Departure. 


No 




Angle. 




N. 


s. 


E. 


w. 


1 

2 
3 
4 
5 


S. S. E.iE. . . 

E. S. E 

S. W. by W. i W. 

W. fN 

S. E. by E. i E. . 


25° 18' 
67° 30' 
61° 52' 
81° 33' 
59° 03' 


16 
23 
36 
12 
41 


1.77 


1447 

8'.80 

17.04 

21.12 


6.83 
21.25 

35.14 


31.71 
11.87 




1.77 


61.43 

1.77 


63.22 
43.58 


43.58 










Diff. 


59.66 


19.64 





Latitude left 

Difference of latitude 59. 



51° 25' K 
miles = 1° 00' S. 



In latitude 60° 25' K 



SEC. Ill] TRAVERSE SAILING. 209 

Then, by formulas for the solution of right-angled tri- 
angles, we have. 

As AG, diff. lat. ar. c. 8.224317 As sin course ar. c. .504995 
departure 19.64 1.293141 : radius 10.000000 

radius, 10.000000 : : departure 19.64 1.293141 



: tang course 18° 13' 9.517458 



distance 62.83 1.798136 



Therefore the direct course is S. 18° 13' E., and the 
distance 62.83 miles. 

OF PLOTTING. 

16. There is yet another method of finding the direct 
course and distance, much practiced by seamen, although 
it does not afford a high degree of accuracy. It is a 
method by plotting, which requires the use of a mariner's 
scale and a pair of dividers. 

One of the scales marked on the mariner's scale, is a 
scale of chords, commonly called a scale of rhumbs, being 
divided to every quarter point of the compass ; and there 
is also a second scale of chords divided to degrees. Both 
of these scales are constructed in reference to the same 
common radius, so that the chords on the scale of rhumbs 
correspond to those on the scale of marked chords. The 
manner of using the scales will appear in plotting the last 
example. 

To construct this traverse, describe a circle with a radius 
equal to the chord of 60° and draw the meridian N/S. 
Then take from the line of rhumbs the chord of the first 
course 2-j points, and apply it from S to 1, to the right of 
NS, since the course is southeasterly, and draw Al ; take, 
in like manner, the chord of the second course, 6 points, 
from ;S' to 2, and lay it off also to the right of the meri- 
dian line. Apply the chord of the third course, 5^ points, 
from S to 3, to the left of the meridian ; the fourth course, 
7i points from iV to 4, to the left of NS, this course be- 
ing northwesterly ; and, lastly, apply the chord of the fifth 
course, 5] points, from S to 5, to the right of N/S, and 
join all the lines as in the figure. 
14 



210 ELEMENTS OF SURVEYING. [BOOK V. 

In the direction Al, lay off the distance AH= 16 miles 
from a scale of equal parts, and through the extremity H, 
draw HG parallel to A2, and lay off HC= 23 miles. Draw 
CD parallel to ^3, and lay off CD =36 miles ; then draw 
DE parallel to J.4, and lay off 12 miles ; and lastly, draw 
EF parallel to J.5, and lay off 41 miles, and F will be the 
place of the ship. Hence, we conclude that AF is the dist- 
ance made good, and GAF is the course. 

Applying, then, the distance AF to the scale of equal 
parts, we find it equal to 62f miles ; and applying the 
chord Sa to the scale of chords, we find the course GAF 
= 18i°. 

2. A ship sails from a place in latitude 24° 32' N., and 
runs the following courses and distances, viz., 1st, S. W. 
by "W. dist. 45 miles ; 2d, E. S. E. dist. 50 miles ; 3d, S. 
W. dist. 30 miles ; 4th, S. E. by E. dist. 60 miles ; 5th, S. 
"W. by S. i W. dist. 63 miles : required her latitude, and 
the direct course and distance from the place left to the 
place arrived at, and the construction of the traverse. 

^^^ j Lat. 22° 3' N., course S. 
^^' I Dist. 149.2 miles. 

3. A ship from lat. 28° 32' K has run the following 
courses, viz., 1st, N. W. by N. 20 miles ; 2d, S. W. 40 miles ; 
8d, N. E. by E. 60 miles ; 4th, S. E. 55 miles ; 5th, W. 
by S. 41 miles ; 6th, E. N. E. 66 miles : required her lat- 
itude, the distance made good, and the direct course, also 
the construction of the traverse. 

Ans. Dist. 70.2 miles, course E. 

4. A ship from lat. 41° 12' N. sails S. W. by W. 21 
miles ; S. W. i S. 31 miles ; W. S. W. i S. 16 miles ; S. 
I E. 18 miles ; S. W. i W. 14 miles ; then W. i N. 30 
miles: required the latitude, the direct course, and the 
distance. 

^^ ( Lat. 40° 05', course S. 52° 49' W. 
■ iDist. 111.7 miles. 

5. A ship runs the following courses, viz.: 

1st, S. E. 40 miles; 2d, N. E. 28 miles; 3d, S W. by 
W. 52 miles ; 4th, N. W. by W. 30 mHes ; 5th, S. S. E. 



SEC. IV.] PARALLEL SAILIN-G. 211 

8Q miles; 6tli, S. E. by E. 58 miles: required the direct 
course, and distance made good. 

^^ ( Direct course S. 25° 59' E., or S. S. E. a E., nearly, 

' (Distance 95.87 miles. 
6. A ship sails, 1st, N. W. by W. i W. 40 miles; 2d, 
K W. by i K, 41 miles ; 3d, N. by E. 16.1 miles ; and 
4tli, K E. i E. 32.5 miles : required the distance made, 
and the direct course. 

Ans. Course, 21° 54' West of North. Dist. 94.6 miles. 
These examples will, perhaps, suffice to illustrate the 
principles of plane sailing. 

The longitude, made on any course, cannot be deter- 
mined by these methods, for this being the arc of the 
equator intercepted between two meridians, cannot be found 
under the supposition that the meridians are parallel. 

The most simple case of finding the difference of lon- 
gitude is when the ship sails due east or due west : this is 
called Parallel Sailing. 



SECTION IV. 

PARALLEL SAILING. 



17. The entire theory of parallel sailing is comprehend- 
ed in the following proposition, viz.: 

The cosine of the latitude of the parallel^ is to radius^ as 
the distance run to the difference of longitude. 

Let IQR represent the equa- 
tor, and FDN any parallel of 
latitude : then, CI will be the 
radius of the equator, and EF 
the radius of the paralleL 

Suppose FD to be the dis- 
tance sailed, then the differ- 
ence of longitude will be meas- 
ured by IQ, the arc intercept- 
ed on the equator. Then, 




212 



ELEMENTS OF SURVEYING. [BOOK V. 




since similar arcs are to eacli 
other as their radii (Geom., 
Bk. v., Prop. 14), we have, 
iJF '. CI :: dist. FD : 
diff. long. IQ. 
But FF is the sine of PF, 
or cosine of FI, the latitude: 
and CI is the radius of the 
sphere : hence, 

cos lat. : i? : : distance : 
difp. longitude. 

18. If we denote by D the distance between any two 
meridians, measured on the parallel whose latitude is L ; 
a/nd by D' the distance between the same meridians meas- 
ured on the parallel whose latitude is L', the arcs are 
similar, and we shall have (Geom,, Bk. Y., Prop. 14), 

cos L : D : : cos L' : D', 
that is, cos L : cos L' : : D : B'. 

Hence, when the longitude made on different parallels is the 
same, the distances sailed are proportional to the cosines of the 
parallels of latitude. 

19. By referring to Th. Y., Bk. I., we see that in any 
right-angled triangle 

B : cos angle at base : : hyp. : base, 
or Gos F : E :: FC : FC ; 
and by comparing this with the propor- 
tion, 
cos lat. : i? : : dist. : diff. long ; 
we see, that if in a right-angled triangle 
the angle at the base be made equal to 
the latitude of the parallel, and the base 
to the distance run ; then, the hypothenuse will represent 
the difference of longitude. 

It follows therefore, that any problem in parallel sail- 
ing, may be solved as a simple case of plane sailing. For, 
if we regard the latitude as the course, the distance run 
as the base, the difference of longitude will be the hypo- 
thenuse of the corresponding right-angled triangle. 




SEC. lY.] PARALLEL SAILING. 213 



EXAMPLES. 

1. A ship from latitude 53° 56' K, longitude 10" 18' 
E., has sailed due west, 236 miles : required her present 
longitude. 

By the rule 

As cos lat. 63° 56' . ar. c. . .230087 

: radius 10.000000 

: : distance 236 . . . . . 2.372912 



: diff. long. 400.8 .... 2.602999 



Long, left . . 10° 18' E. 
Diif. long. = -^ degrees = 6° 40' W. 

Long. . . 3° 38' E. 



2. If a ship sails B, 126 miles from the North Cape, 
in lat. 71° 10' IST., and then due N., till she reaches lat, 
73° 26' IST. ; how far must she sail W. to reach the meri- 
dian of the North Cape ? 

Here the ship sails on two parallels of latitude, first on 
the parallel of 71° 10', and then on the parallel of 73° 26', 
and makes the same difference of longitude on each parallel. 

Hence, by Art. 18, 

As cos lat. 71° 10' arith. comp. 0.491044 
: distance 126 . . 2.100371 

: : cos lat. 73° 26' . . 9.455044 



: distance 111.3 . . 2.046459 



3. A ship in latitude 32° K sails due E. till her dif- 
ference of longitude is 384 miles : required the distance 
run. Ans. 325.6 miles. 

4. If two ships in latitude 44° 30' N., distant from 
each other 216 miles, should both sail directly S. till their 
distance is 256 miles, what latitude would they arrive at? 

Ans. 32° 17' N. 



214 N'AVIGATION. [BOOK V. 

5. Two ships in the parallel of 47° 54' K, have 9° 35' 
difference of longitude, and they both sail directly S., a 
distance of 836 miles: required their distance from each 
other at the parallel left, and at that reached. 

Am. 385.5 miles, and 479.9 miles. 



SECTION V. 

MIDDLE LATITUDE SAILING. 



20. Having seen how the longitude which a ship makes 
when sailing, on a parallel of latitude may be determined, 
we come now to examine the more general problem, viz., 
to find the longitude which a ship makes when sailing 
upon any oblique rhumb. 

There are two methods of solving this problem, the one 
by what is called middle latitude sailing, and the other by 
Mercator's sailing. The first of these methods is confined 
in its application, and is moreover somewhat inaccurate 
even where applicable ; the second is perfectly general, and 
rigorously true ; but still there are cases in which it is advi- 
sable to employ the method of middle latitude sailing, in 
preference to that of Mercator's sailing. It is, therefore, 
proper that middle latitude sailing should be explained, 
especially since, by means of a correction to be hereafter 
noticed, the usual inaccuracy of this method may be 
rectified. 

Middle latitude sail- 
ing proceeds on the 

supposition that the de- y^ '^VXX'S^^^ 

parture or sum of all 
the meridional distan- 
ces, h% c'c, did, &c., 
from to T, is equal 
to the distance M'M 
between the meridians 
passing through and T, measured on the parallel of lati- 
tude equally distant from and T. 




SEC. v.] MIDDLE LATITUDE SAILING. 215 

The middle latitude is half the sum of tlie two extreme 
latitudes, if they are both of the same name, and half 
their difference, if they are of contrary names. 

The supposition above becomes very inaccurate when the 
course is small, and the distance run great ; for it is plain that 
the middle latitude distance will receive a much greater acces- 
sion than the departure, if the track OT cuts the successive 
meridians at a very small angle. 

The principal approaches nearer to accuracy as the angle 
of the course increases, because then as but little ad- 
vance is made in latitude, the several component depart- 
ures lie more in the immediate vicinity of the parallel M'M. 
But still, in very high latitudes, a small advance in lat- 
itude makes a considerable difference in meridional dist- 
ance ; hence, this principle is not to be used in such lat- 
itudes, if much accuracy is required. 

By means, however, of a small table of corrections, con- 
structed by Mr. Workman^ the imperfections of the middle 
latitude method may be removed, and the results of it ren- 
dered in all cases accurate. This table we have given at 
the end of this work. 

21. The rules for middle latitude sailing may be thus 
deduced. 

We have seen, in the first case of plane 
sailing, that if a ship sails on an oblique 
rhumb from to T, that the hypothenuse 
OT will represent the distance ; OT' the 
difference of latitude, and T'T^ the depart- 
ure. Now, by the present hypothesis, 
the departure T'T is equal to the middle 
parallel of latitude between the meridians 
of the places sailed from and arrived at : 
so that the difference of longitude of these two places is the 
same as if the ship had sailed the distance T'T on the mid- 
dle parallel of latitude. The determination of the differ- 
ence of longitude is, therefore, reduced to the case of par- 
allel sailing: for, T'T now representing the distance on the 
parallel, if the angle T'TO' be made equal to the latitude of 




216 NAVIGATION. [BOOK V. 

that parallel, we shall have, by the last case, the difference 
of longitude represented by the hypothenuse O'T. We 
therefore have the following theorems: 

I. In the triangle O'TT', 

cos O'TT' : TT' : : B : T0'\ 
that is, 

cos mid. lat. : departure : : R \ diff. longitude. 

II. In the triangle O'TO 

sin 0' : OT : : sin : O'T] 
that is, since sin 0' = cos O'TT' 
cos mid. lat. : distance : : sin. course : diff. longitude. 

III. In the triangle OTT', we have 

B : tangent : : OT' : TT' ; 
comparing this with the first proportion, and observing 
that the extremes of this are the means of that, we have 

OT' : O'T :: cos O'TT' : tang 0; 
that is, 
diff. lat. : diff. long. : : cos mid. lat. : tang course. 

These three propositions comprise the theory of mid- 
dle latitude sailing ; and when to the middle latitude sail- 
ing, the proper correction, taken from Mr. Workman's table, 
is applied, these theorems will be rendered accurate. 

In the table of pages 93 and 94, the middle latitude is 
to be found in the first column to the left. Then, along 
the horizontal Hue, and under the given difference of lat- 
itude, is inserted the proper correction to be added to the 
middle latitude to obtain the latitude in which the meri- 
dian distance is accurately equal to the departure. Thus, 
if the middle latitude be 37°, and the difference of latitude 
18°, the correction will be found on page 94, and is equal 
to 0° 40'. 

EXAMPLES. 

1. A ship, in latitude 51° 18' N., longitude 22° 6' W., 
is bound to a place in the S. E. quarter, 1024 miles dis- 
tant, and in lat. 37° N. : what is her direct course and dis- 



SEC. v.] MIDDLE LATITUDE SAILING. 



217 



tance, as also the clijBference of longitude between the two 
places ? 

Lat. from 51° 18' K 



Lat. to 87° N. 



Sum of latitudes . 
Mid. lat. . . . 



. 88° 18' 
. 44° 9' 



Diff. lat. 14° 18 = 858 miles. 



As distance 1024 

: radius 

: : diff. lat. 858 



6.989700 

10.000000 

2.933487 



cos course 33° 5' 9.923187 



Cos mid lat 44° 9' ar c 0.144167 
: tang course 33° 5' 9.813899 
: : diff. lat. 858 2.933487 



diff. long. 779 2.891553 



In this operation the middle latitude has not been cor- 
rected, so that the difference of longitude here determined 
is not without error. To find the proper correction, look 
for the given middle latitude, viz., 44° 9', in the table of 
corrections, the nearest to which we find to be 45° ; against 
this and under 14° diff. of lat, we find 27' ; and also, under 
15° we find 31', the difference between the two being 4' ; 
hence, corresponding to 14° 18' the correction will be about 
28'. Hence, the corrected middle latitude is 44° 37', 
therefore, 

Cos corrected mid. lat. 44° 37' ar. comp. 0.147629 
: tang, course 33° 5' . . 9.813899 

: : diff. lat. 858 . . . 2.933487 



diff. long 



785.3 



. 2.895015 



2. A ship sails in the IST. "W. quarter, 248 miles, till her 
departure is 135 miles, and her difference of longitude 310 
miles : required her course, the latitude left, and the lat- 
itude come to. 



) Course K 32° 59' W. ; 



Lat. left 62° 27' K; lat. in 65° 55' K 
3. A ship, from latitude 37° N., longitude 9° 2' W., 
having sailed between the N. and W., 1027 miles, reckons 
that she has made 564 miles of departure : what was her 
direct course, and the latitude and longitude reached? 

. (Course K 38° 19' W., or K W. nearly; 
' I Lat. 51° 18' K ; long. 22° 8' "W. 



218 NAVIGATION. [BOOK V. 

4. Required tlie course and distance from the east point 
of St. Michael's, lat. 87° 48' K, long. 25° 13' W., to the 
Start Point, lat. 50° 13' K, long. 3° 38' W. ; the middle 
latitude being corrected by Workman's table, 

Ans. Course K 51° 11' B. ; dist. 1189 miles. 

mercatoe's sailing. 

22. It has already been observed, that when a ship 
sails on an oblique rhumb, the departure, the difference of 
latitude, and the distance run, are truly represented by 
the sides of a right-angled triangle. 

Thus, if a ship sails from A to B, the 
departure B'B will represent the sum of 
all the very small meridian distances, 
or elementary departures, b'b, p"_p, &c. ; 
the difference of latitude AB will re- 
present, in like manner, the small dif- 
ferences of latitude Ab\ h'p\ &c. ; and 
the hypothenuse AB, will express the 
sum of the distances corresponding to 
these several differences of latitude 
and departure. Each of these elements is supposed to be 
taken so small, as to form on the surface of the sphere a 
series of triangles, differing insensibly from plane triangles. 

Let ABB' be a triangle, in which the angle A repre- 
sents the course, AB' the difference of latitude, B'B the 
departure, and AB the distance run. Produce the side 
AB to C, until CC shall be equal to the difference of 
longitude of the two extremities of the course : then, for 
the sake of distinction, we call 

AB' = the proper difference of latitude, 
AC = the meridional difference of latitude, 
and we are now to explain the manner of constructing a 
table, called a table of meridional parts, which will furnish 
the meridional differences of latitude, when the ^proper differ- 
ences are known. 

Let Ah'h represent one of the elementary triangles ; h'h 
will then be one of the elements of departure; and AV 
the corresponding difference of latitude. Now, as Vh is a 
small arc of a parallel of latitude, it is to a portion of the 




SEC. v.] MERCATOR'S SAILIlfG. 219 

equator containing an equal number of degrees, as the co- 
sine of its latitude is to radius (Art. 17). This similar 
portion of the equator, is the difference of longitude be- 
tween h' and h. 

Suppose, now, that Ah' is prolonged to p', making p'p 
equal to the difference of longitude between h and h' : then 
W : pp' : : cos lat. I'h : R (Art. 17.) 

But, by similar triangles, we have 

W : pp' : : Ah' : Ap', 
and consequently, 
proper lat. Ah' : mer. dijff. of lat. Ap' : : cos lat. hh' : 1. 

Denoting the proper difference of latitude by d, the 
meridional difference of latitude by D, the latitude of h'h 
by Z, and the radius by 1, which is, indeed, the radius of 
the table of natural sines, we shall have 

c? : Z) : : cos Z : 1, 
which gives 

D — d secant I, since ^ = sec. I. 

' cos I 

K then, we know the latitude I of the beginning of a 
course, and the proper difference of latitude d of the ex- 
tremity of the course, we can easily find the meridional 
latitude D corresponding to that course. 

The determination of AC which represents the meri- 
dional difference of latitude, involves the determination of 
all the elementary parts, on which it depends. If d be 
taken equal to 1', we shall have from the equation above 

D=V sec. ?, or D = sec. 1, 

it being understood that I expresses minutes or geographi- 
cal miles. 

From this equation, the value of D^ corresponding to 
every minute of ?, from the equator to the pole, may be 
calculated ; and from the continued addition of these, there 
may be obtained, in succession, the meridional parts cor- 
responding to 1', 2', 3', 4', &c., of proper latitude, and when 
registered in a table, they form a table of meridional parts, 
given in all books on Navigation. 

The following may serve as a specimen of the manner 
in which such a table may be constructed, and, indeed, of 
the manner in which the first table of meridional parts was 



220 NAVIGATION. [BOOK V. 

actually formed by Mr. Wriglit, tlie proposer of this valu- 
able metliod. 

Mer. pts. of V - nat. sec. 1'. 
Mer. pts. of 2' = nat. sec. 1' + nat. sec. 2'. 
Mer. pts. of 3' = nat. sec. 1' + nat. sec. 2' + nat. sec. S'. 
Mer. pts. of 4' = nat. sec. 1' + nat. sec. 2' + nat. sec. 8' + &c. 
Hence, by means of a table of natural secants we have 

Nat. Sees. Mer. Pts. 

Mer. pts. of 1' = 1.000000 = 1.0000000 

Mer. pts. of 2' = 1.0000000 + 1.0000000 = 2.0000002 
Mer. pts. of 3' = 2.0000002 + 1.0000004 = 8.0000006 
Mer. pts. of 4' = 3.0000006 + 1.0000007 = 4.0000013, &c. 
There are other methods of construction, but this is the 
most simple and obvious. The meridional parts thus de- 
termined, are all expressed in geographical miles, because 
in the general expression 

D = l' sec. 2, 
1' is a geographical mile, 

23. Having thus formed the table of meridional parts, 
if we find from it, the meridional parts corresponding to 
the latitudes of the place left and the place arrived at, 
their difference will be the meridional difference of lat- 
itude, or the line AC in the diagram. The difference of 
longitude denoted by CO may then be found by the fol- 
lowing proportion. 

I. As radius is to the tangent of the course, so is the meri- 
dional difference of latitude to the difference of longitude. 

But if the departure be given instead of the course, then, 

II. As the proper difference of latitude is to the departure, 
so is the meridional difference of latitude to the longitude. 

Other proportions may also be deduced from the diagram. 

EXAMPLES. 

As an example of Mercator's or rather Wright's, sailing, 
let us take the following : 

1. Eequired the course and distance from the east point 
of St. Michael's to the Start point: the latitudes being 87° 
48' N., and 50° 13' K, and the longitudes 25° 13' W., and 
3° 38' W. 



SEC. v.] 



MERCATOR'S CHART. 



Start Point, lat. 50° 13' K 
St. Michaers, lat. 37° 48' K 



Proper difference of lat. 12° 25 
60 



Mer. pts. 8495 
Mer. pts, 2453 

Mer. diflf. 1042 



_ Diff. oflong. 21° 35' 

Diff. in miles 745 60 

Diff. in miles 1295 



Now, let us suppose that we liave 
sailed from A to B: we shall tlien 
know AB' equal proper diflf. lat. = 745 
miles ] AC = meridional diff. of lat. = 
1042; and 0'0 = the difference of lon- 
gitude equal to 1295 miles. It is re- 
quired to find the course B'AB, and the 
distance AB. 




For the Course. 

As AC 1042 6.982132 

: radius 10.000000 

:: CC 1295 3.112270 



: tang. A 51° 11' E. 10.094402 



For the Distance. 

As cos A 51° 11' 0.202850 
: AB' 745 2.872156 

: : radius 10.000000 



AB 1189 



3.075006 



2. A ship sails from latitude 37° N. longitude 22° 56' 
W., on the course N. 33° 19' E. : till she arrives at 51° 
18' N. : required the distance sailed, and the longitude ar- 
rived at. Am. Dis. 1027 miles ; long. 9° 45' W. 

MEEOATOR's CHART. 

24. Mercator's Chart is a Map constructed for the use 
of Navigators. In this chart all the meridians are repre- 
sented by straight lines drawn parallel to each other, and 
the parallels of latitude are also represented by parallel 
straight lines drawn at right-angles to the meridians. 

The chart may be thus constructed. Draw on the lower 
part of the paper a horizontal line to represent the parallel 
of latitude which is to bound the southern portion of the 
chart. From a scale of equal parts, corresponding in size 



222 NAVIGATION. [BOOK V. 

to the extent of tlie map to be made, lay off, on this line, 
any number of equal distances, and tbrongli the points 
draw a series of parallels to represent the meridians. 

Then draw a line on the side of the map, and for the 
second parallel of latitude, find from the table of meri- 
dional parts the meridional difference of latitude corres- 
ponding to the degrees between the first and second par- 
allel, and lay off this distance for the interval between the 
two parallels. Then find the meridional difference between 
the second and third, and lay it off in the same way for 
the third parallel, and so on, for the fourth, fifth, &c. 

A place whose latitude and longitude are known, may 
be laid down in the same manner; for it will always be 
determined by the intersection of the meridian and parallel 
of latitude. 

If the chart is constructed on a small scale, the divisions 
on the graduated hues, may be degrees instead of minutes ; 
and the meridians and parallels may be drawn only for 
every fifth or tenth degree. 

We have already seen (Art, 23), that the meridional 
difference of latitude bears a constant ratio to the difference 
of longitude, so long as the course remains unchanged : 
and hence we see that on Mercator's chart, every rhumb 
will be represented by a straight line, 

LINE OF MERIDIONAL PARTS ON GUNTER's SCALE. 

25. This scale corresponds exactly with the table of me- 
ridional parts, excepting, that in the table, the circle is divid- 
ed to minutes, while the scale is divided only to degrees. 
A scale of equal parts is placed directly beneath the scale 
of meridional parts ; if the former corresponds to divisions 
of longitude, the latter will represent those of latitude. 
Hence, a chart may be constructed from those scales, by 
using the scale of equal parts for the lines of longitude, 
and the scale of meridional parts for those of latitude. 



A TABLE 

OF 

LOGARITHMS OF NUMBERS 

FEOM 1 TO 10,000. 



N. 


Log. 


N. 


Log. 


N. 


Log. 


N. 


Log. 


I 


0-000000 


26 


1-414973 ■ 


5i 1 


-707570 


76 1 


880814 


2 


o-3oio3o 


27 


i.43i364 


52 1 


•716008 


77 I 


886491 


3 


0-477121 


28 


1.447158 


53 I 


724276 


78 1 


892095 


4 


0-602060 


29 


1.462898 


54 1 


782394 


79 I 


897627 


5 


0-698970 


3o 


1-477121 


55 I 


740868 


80 I 


908090 


6 


o-778i5i 


81 


1-491862 


56 I 


748188 


8x 1 


908485 


7 


0-845098 


32 


i.5o5i5o 


tl \ 


755875 


82 I 


918814 


8 


0-908090 


33 


i.5i85u 


768428 


83 1 


919078 


9 


0-954243 


34 


1-531479 


59 1 


770852 


84 1 


924279 


10 


I -000000 


85 


1.544068 


60 1 


778151 


85 1 


929419 


,1 


I -041393 


36 


i.5563o8 


61 1 


785330 


86 I 


934498 


12 


I-079I8I 
i- 118943 


37 


1-568202 


62 1 


792892 


87 1 


989519 
944483 


i3 


38 


1-579784 


63 1 


799341 


88 I 


14 


1.146128 


39 


1-591065 


64 1 


806181 


89 I 


949390 


i5 


1-176091 


40 


1-602060 


65 1 


812918 


90 1 


954243 


i6 


1-204120 


41 


1-612784 


66 1 


819544 


91 1 


959041 


n 


I -230449 


42 


1-628249 


tl \ 


826075 


92 I 


968788 


i8 


1-255273 


48 


1-688468 


882509 


93 1 


968483 


19 


1-278754 


44 


1-643453 


69 1 


838849 


94 I 


978128 


20 


i-3oio3o 


45 


1-653213 


70 1 


845098 


95 1 


977724 


21 


1-322219 


46 


1-662758 


71 1 


851258 


96 I 


982271 


22 


1-842423 


47 


1-672098 


72 I 


857383 


97 I 


986772 


23 


1.861728 


48 


1-681241 


73 I 


868323 


98 I 


991226 


24 


I-3802II 


49 


1-690196 


74 I 


869282 
875061 


99 I 


995635 


25 


1.397940 


5o 


1-698970 


75 1 


100 2 


000000 



Remark. In the following table, in the nine right hand 
columns of each page, where the first or leading figures 
change from 9's to O's, points or dots are introduced in- 
stead of the O's, to catch the eye, and to indicate that from 
thence the two figures of the Logarithm to be taken from 
the second column, stand in the next line below. 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



N. 





' 


2 


3 


4 


5 


6 


7 


8 


9 


D. 


100 


000000 


0434 


0868 


i3oi 


1734 


2166 


2598 


3029 


3461 


3891 


432 


lOI 


4321 


4751 


5i8i 


5609 


6o38 


6466 


6894 


7321 


7748 


8174 


428 


102 


8600 


r.il 


& 


9876 


•3oo 


•724 


1147 


1570 


1993 


24i5 


424 


io3 


012837 


4100 


4521 


4940 


536o 


5779 


6197 


6616 


n 


104 


7033 


745i 


7868 


8284 


X 


9116 

3252 


9532 
3664 


9947 


•36i 


•775 


io5 


021189 
53o6 


i6o3 


2016 


2428 


4075 


4486 


4896 


All 


io6 


5715 


6125 


6533 


6942 


7350 


7757 


8164 


8571 


8978 


408 


:o^ 


9384 
033424 


Til 


•195 


•600 


1004 


1408 


1812 


2216 


2619 


3021 


404 


4227 
8223 


4628 


5029 


543o 


5830 


6230 


6629 


7028 


400 


109 


7426 


7825 


8620 


9017 


9414 


9811 


•207 


•602 


•998 


396 


no 


041393 


1787 


2182 


2576 


Itsl 


3362 


3755 


4148 


4540 


8830 


3^ 


III 


5323 


5714 


6io5 


64o5 


V,ll 


7664 


8o53 


8442 


112 


9218 
053078 


9606 


mi 


•3§o 


•766 


1538 


1924 


2309 


2694 


386 


ii3 


3463 


423o 


46x3 


4996 


5378 


5760 


6142 


6524 


382 


114 


6905 


7286 


7666 


8046 


8426 


8§o5 


9i85 


9563 
3333 


9942 


•320 


379 


ii5 


060698 


io75 


1452 


1829 


2206 


2582 


2958 


3709 


4o83 


376 


116 


4458 


4832 


5206 


558o 


5953 


6326 


6699 


7071 


7443 


78i5 


372 


\\l 


8186 


8557 


8928 


6640 


9668 


••38 


•407 


•776 


1145 


i5i4 


^S 


071882 


225o 


2617 


3352 


3718 


4085 


445 1 


4816 


5i82 


119 


5547 


5912 


6276 


7004 


7368 


7731 


8094 


8457 


8819 


363 


120 


079181 


9543 
3i44 


9904 
35o3 


•266 


•626 


Til 


1347 


1707 


2067 


2426 


36o 


121 


082785 


3861 


4219 


4934 


5291 


9198 


6004 


357 


122 


636o 


6716 


7071 


7426 


7781 


8i36 


8490 


8845 


tf, 


355 


123 


9905 
093422 


•258 


•611 


»963 


i3i5 


1667 


2018 


2370 


2721 


35i 


124 


3772 


4122 


4471 


4820 


5169 


55i8 


5866 


62i5 


6562 


349 


125 


6910 


7257 


7604 


7951 


8298 


8644 


5S 


9335 


9681 


••26 


346 


126 


100371 


0715 


1059 


i4o3 


1747 


2091 


2777 


3119 


3462 


343 


IS 


38o4 


4146 




4828 


5169 
8565 


55io 


585: 


6191 


6531 


687, 


340 


7210 


7549 


7888 


8227 


8903 


9241 


9579 


9916 


•253 


338 


129 


110590 


0926 


1263 


1599 


1934 


2270 


2605 


2940 


3275 


3609 


335 


i3o 


1 13943 


4277 


461 1 


4944 


5278 


56ii 


5943 


6276 
9586 


6608 


6940 


333 


i3i 


7271 


7603 


7934 


8265 


8595 


8926 


9256 


9915 


•245 


33o 


I32 


120574 


0903 


I23l 


i56o 


1888 


2216 


2544 


2871 


3198 
6456 


3525 


328 


i33 


3852 


4178 


45o4 


483o 


5i56 


5481 


58o6 


6i3i 


6781 


325 


i34 


7io5 


7429 


7753 


8076 


8399 


8722 


9045 


9368 


9690 


••12 


323 


i35 


i3o334 


o65d 


0977 


1298 


1619 


1939 


2260 


258o 


2900 


3219 


321 


i36 


3539 


3858 


4177 


4496 


4814 


5i33 


545 1 


5769 


6086 


64o3 


3i8 


137 


6721 


7037 


7354 


7671 


7987 


83o3 


8618 


8934 


9249 


9064 


3i5 


138 


•194 


•5o8 


•822 


1136 


i45o 


1763 


2076 


2389 


2702 


3i4 


139 


3327 


3639 


3951 


4263 


4574 


4885 


5,96 


5507 


58i8 


3ii 


140 


I46I28 


6438 


6748 


7o58 


7367 


7676 


79B5 


8294 


86o3 


8911 


309 


Ui 


Jlii 


9527 


9835 


•142 


•449 


•756 


io63 


1370 


1676 


1982 


307 


142 


2594 


2900 


32o5 


35io 


38i5 


4120 


4424 


4728 


5o32 


3o5 


143 


5336 


5640 


5943 


6246 


6549 


6852 


7154 


7457 


7759 


8061 


3o3 


144 


8362 


8664 


8965 


9266 


9567 


9868 


•168 


•469 


•769 


1068 


3oi 


145 


i6i368 


1667 


1967 


2266 


2564 


2863 


3i6i 


3460 


3758 


4o55 


299 


146 


4353 


465o 


4947 


5244 


5541 


5838 


6i34 


6430 


6726 


7022 


297 


U7 


7317 


7613 


7908 


8203 


8497 
1434 


8792 


9086 


9380 


9674 


tl 


295 


148 


170262 


o555 


0848 


1141 


1726 


2019 


23ll 


26o3 


293 


149 


3i86 


3478 


3769 


4060 


435i 


4641 


4932 


5222 


55i2 


58o2 


291 


i5o 


176091 


638i 


6670 


S 


7248 


7536 


7825 


8ii3 


8401 


8689 
1 558 


289 


i5i 


181844 


9264 


9552 


•126 


•4i3 


S? 


•985 

3839 


1272 


287 


l52 


2129 
4075 


24i5 


2700 


2985 
5825 


3270 


4123 


4407 


285 


1 53 


4691 


5259 


5542 


6108 


6391 


6674 


6956 


7239 


283 


1 54 


7521 


7803 


8084 


8366 


8647 


8928 


9209 


9490 


9771 


••5i 


281 


i55 


190332 


0612 


& 


3^ 


i45i 


1730 


2010 


2289 


2567 


2846 


279 


1 56 


3i25 


3403 


4237 


45i4 


4792 


5069 


5346 


5623 


278 


1 57 


a 


6176 


6453 


6729 


70o5 


7281 


7556 


7832 


8107 


8382 


276 


1 58 


8932 


9206 


9481 


9755 


••29 


•3o3 


•577 


•85o 


1124 


274 


159 


201397 


1670 


1943 


2216 


2488 


2761 


3o33 


33o5 


3577 


3848 


272 


N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


D. 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



N. 


j I 


2 


3 


4 


5 


6 


7 1 8 


9 


D. 


1 60 


204120' 4391 


4663 


4934 


5204 


5475 


5746 


6016 


6286 


6556 


271 


161 


6826: 7006 
gSiD 9783 


7365 


7634 


7904 


8173 


8441 


8710 


8979 


9247 


269 


162 


••5i 


•319 


•586 


•853 


1121 


i388 


1654 


1921 


267 


i63 


212188; 2454 


2720 


2986 


3252 


35i8 


3783 


4049 


43i4 


4579 


266 


164 


4844; 5109 


5373 


5638 


5902 


6166 


6430 


6694 


6957 


7221 


264 


i65 


7484, 7747 


8010 


8273 


8536 


8798 


9060 


9323 


9585 


9846 


262 


166 


220108 0370 


o63i 


0892 


ii53 


1414 


1675 


lilt 


2196 


2456 


261 


167 


2716 2976 
5309! 5568 


3236 


3496 


6342 


4oi5 


4274 
6858 


4792 


5o5i 


259 


168 


5826 


6084 


6600 


71.5 


7372 


7630 


258 


169 


7887J 8144 


8400 


8657 


8913 


9170 


9426 


9682 


9938 


•■93 


256 


170 


230449 0794 


0960 


I2l5 


1470 


1724 


1979 


2234 


2488 


2742 


254 


171 


5^23! 5781 


35o4 


3757 


4011 


4264 


4517 


4770 


5o23 


5276 


253 


172 


6o33 


6285 


6537 


6789 


7041 


7292 


7544 


7795 


252 


173 


8046 


8297 


8548 


8799 


9049 


9299 


9550 


9800 


••5o 


•3oo 


25o 


174 


240549 


0799 


1048 


1297 


1 546 


179D 


2044 


2293 


2541 


2790 


249 


175 


3o3S 


3286 


3534 


3782 


4o3o 


4277 


4525 


4772 


5019 


5266 


248 


176 


55i3 


5759 


6006 


6252 


6499 


6745 


6991 


7237 


7482 


7728 


246 


177 


7973 


8219 


8464 


8709 


8954 
1395 


9198 


9443 


9687 


Its 


•176 


245 


178 


25o420 


0664 


0908 


ii5i 


1638 


1881 


2125 


2610 


243 


179 


2853 


3096 


3338 


358o 


3822 


4064 


43o6 


4548 


4790 


5o3i 


242 


180 


255273 


55i4 


5755 


5996 


6237 


6477 


6718 


6958 


7198 


3g? 


241 


181 


7679 


7918 
o3io 


8i58 


07^? 


8637 


8877 


9116 


9355 


9594 


III 


182 


260071 


o548 


1025 


1263 


i5oi 


1739 


1976 
4346 


2214 


1 83 


245 1 


2688 


2925 


3162 


3399 


3636 


3873 


4109 


4582 


237 


184 


4818 


5o54 


5290 


5525 


5761 


5996 


6232 


6467 


6702 


6937 


235 


1 85 


7172 


7406 


7641 


7875 


8110 


8344 


8578 


8812 


9046 


9279 


234 


186 


95i3 


9746 


9980 


•2l3 


•446 


•679 


•912 


1144 


1377 


1609 


233 


187 


271842 


2074 
4389 


23o6 


2538 


2770 


3ooi 


3233 


3464 


3696 


3927 


232 


188 


4i58 


4620 


485o 


5o8i 


53ii 


5542 


5772 


6002 


6232 


23o 


189 


6462 


6692 


6921 


7i5i 


7380 


7609 


7838 


8067 


8296 


8525 


229 


190 


278754 


8982 


9211 


9439 


9667 


9895 
2169 


•123 


•35i 


•578 


•806 


228 


191 


281033 


1261 


1488 


1715 


1942 


2396 


2622 


2849 


3075 


227 


192 


33oi 


3527 


3753 


Itll 


42o5 


443i 


4656 


4882 


5107 


5332 


226 


193 


5557 


5782 


6007 


6456 


6681 


6905 


7i3o 


7354 


7578 


225 


194 


7802 


8026 


8249 


8473 


8696 


8920 


9143 


9366 


ffi 


9812 


223 


195 


290035 


0257 


0480 


0702 


0925 


1147 


i369 


1591 


2o34 


222 


196 


2256 


2478 


2699 


2920 


3i4i 


3363 


3584 


38o4 


4025 


4246 


221 


197 


4466 


4687 


4907 


5127 


5347 


5567 


5787 


6007 


6226 


6446 


220 


198 


6665 


6884 


7104 


7323 


7542 


7761 


7979 


8198 


8416 


8635 


219 


199 


8853 


9071 


9289 


9507 


9725 


9943 


•161 


•378 


.595 


•8i3 


218 


200 


3oio3o 


1247 


1464 


i68i 


4059 


2114 


233i 


2547 


2764 


2980 


217 


201 


3ig6 


3412 


3628 


3844 


4275 


4491 
6639 


4706 


4921 


5i36 


216 


202 


535i 


5566 


5781 


5996 


6211 


6425 


6854 


7068 


7282 


2l5 


203 


7496 


7710 


7924 


8137 


835i 


8564 


8778 


8991 


9204 


9417 


2l3 


204 


9630 


9843 


••56 


•268 


•481 


•693 


•906 


1118 


i33o 


1 542 


212 


205 


311754 


1966 


2177 


2389 


2600 


2812 


3o23 


3234 


3445 


3656 


211 


206 


3867 


4078 


4289 


4499 


4710 


4920 


5i3o 


5340 


555i 


5760 


210 


207 


5970 


6180 


6390 


6599 


7018 


7227 


7436 


7646 


7854 


209 


208 


8o63 B272 


8481 


8689 


9106 


9314 


9322 


9730 


9938 


20a 


209 


320146 


o354 


o562 


0769 


0977 


1184 


1391 


1598 


i8o5 


2012 


207 


210 


322219 


2426 


2633 


2839 


3046 


3252 


3458 


3665 


3871 


4077 


206 


211 


4282 


4488 


4694 


4899 
6930 


5io5 


53io 


55i6 


5721 


5926 


6i3i 


2o5 


212 


6336 


6541 


6745 


7155 


g? 


7563 


7767 


7972 


8176 


204 


2l3 


838o 


8583 


8787 


8991 


9194 


9601 


9805 


•••8 


•211 


203 


214 


33o4i4 


0617 


0819 


1022 


1225 


1427 


i63o 


i832 


2o34 


2236 


202 


2l5 


2438 


2640 


2842 


3044 


3246 


3447 


3649 


385o 


4o5i 


4253 


202 


216 


4454 


4655 


4856 


5o57 


5257 


5458 


5658 


5859 


6059 


6260 


201 


217 


6460 


6660 


6860 


7060 


7260 


7459 


7659 


7858 


8o58 


8257 


200 


218 


8456 


8656 


8855 


9054 


9253 


945 1 


9650 


9849 


••47 


•246 


199 


219 


340444 


0642 


0841 


1039 


1237 


1435 


i632 


i83o 


2028 


2225 


198 


N. 





I 


2 


' 


4 


5 


6 


7 


8 


9 


D. 



15 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



N. 


1 I 


2 


3 


4 


5 


6 


7. 


8 


9 


D. 


220 


342423 


2620 


4785 


3oi4 


3212 


3409 


36o6 


38o2 


3999 


4196 
607 


197 


221 


4392 
6353 


4589 


4981 


5178 


% 


5570 


5766 


5^62 


i?6 


222 


6549 


6744 


6939 


7135 


7525 


7720 


79i5 


8uo 


195 


223 


83o5 


85oo 


8694 


8889 


9083 


9278 


9472 


9666 


9860 


••54 


194 


224 


350248 


0442 


o636 


0829 


1023 


1216 


1410 


i6o3 


1796 


1989 
3916 


193 


225 


2i83 


2375 


2568 


2761 


2954 


3i47 


3339 


3532 


3724 


193 


226 


4108 


43oi 


4493 


4685 


4876 


5o68 


5260 


5452 


5643 


5834 


192 


227 


6026 


6217 


6408 


6599 


6790 


6981 


7172 


7363 


7554 


7744 


191 


228 


7935 


8125 


83i6 


85o6 


8696 


8886 


9076 


9266 


9456 


9646 


190 


229 


9835 
361728 


••25 


•2l5 


•404 


0593 


•783 


•972 


1161 


i35o 


1539 


189 


230 


1917 


2io5 


2294 


2482 


2671 


2859 


3048 


3236 


3424 


188 


23l 


36i2 


38oo 


3988 


4176 


4363 


455i 


4739 


4926 


5ii3 


53oi 


188 


232 


5488 


5675 


5862 


6049 


6236 


6423 


6610 


86? 
•5i3 


6983 


7169 


187 


233 


7356 


7542 


7729 


791D 


8101 


8287 


8473 


8845 


9o3o 


186 


234 


9216 


9401 


9587 


9772 


"& 


•143 


•328 


•698 


•883 


i85 


235 


371068 


1253 


1437 


1622 


1991 


2175 


236o 


2544 


2728 


184 


236 


2912 


4932 


3280 


3464 


3647 


383i 


401 5 


4198 


4382 


4565 


184 


237 


4748 


5ii5 


5298 


5481 


5664 


5846 


6029 


6212 


6394 


1 83 


238 


6577 


ttt 


6942 


7124 


7306 


7488 


7670 


7852 


8o34 


8216 


182 


239 


8398 


8761 


8943 


9124 


9306 


9487 


9668 


9849 


••3o 


181 


240 


38021 1 


0392 


0573 


0754 


0934 


iii5 


1296 


1476 


1 656 


1837 


181 


241 


2017 


2197 


2377 


2557 


2737 


2917 


3097 


3277 


3456 


3636 


180 


242 


38i5 


3995 


4174 
5964 


4353 


4533 


4712 


4891 


5070 


5249 


5428 


179 


243 


56o6 


5785 


6142 


6321 


6499 


6677 


6856 


7034 
8811 


7212 


178 


244 


7390 


7568 


7746 


7923 


8101 


8279 


8436 


8634 


8989 


178 


245 


9166 


9343 


9520 


9698 


9875 


••5 1 


•228 


•4o5 


•582 


•759 


177 


246 


390935 


1112 


1288 


1464 


1641 


1817 


1993 


2169 


2345 


2521 


176 


247 


4452 


2873 


3048 


3224 


3400 


3575 


\t\ 


3926 


4101 


4277 


176 


248 


4627 


4802 


4977 


5i52 


5326 


5676 


5850 


6025 


175 


249 


6199 


6374 


6548 


6722 


6896 


7071 


7245 


7419 


7592 


7766 


174 


25o 


397940 


8.14 


8287 


8461 


8634 


8808 


8981 


9154 


9328 


95oi 


173 


25l 


9674 


9847 


••20 


• 192 


•365 


•538 


•7.1 


*883 


Jo56 


1228 


173 


252 


401401 


1573 


1745 


1917 


2089 


2261 


2433 


26o5 


2777 


2949 


172 


253 


3l2I 


3292 


3464 


3635 


3807 


3978 


4i'49 


4320 


4492 


4663 


171 


254 


4834 


5oo5 


5.76 


5346 


5517 


5688 


58D8 


6029 


6199 


6370 


171 


255 


6540 


6710 


6881 


8749 


7221 


7391 


756i 


7731 


7901 


8070 


170 


256 


8240 


8410 


8579 


8918 


9087 


9237 


9426 




9764 


169 


257 


9933 


•102 


•271 


•440 


:5 


•777 


•946 


1114 


1283 


i45i 


169 


258 


411620 


1788 


1956 


2124 


2461 


2629 
43o5 


2796 


2964 


3i32 


168 


259 


33oo 


3467 


3635 


38o3 


3970 


4i37 


4472 


4639 


4806 


167 


260 


414973 


5i4o 


5307 


5474 


5641 


58o8 


^n^o 


6141 


63o8 


6474 


167 


261 


6641 


6807 


6973 
8633 


7i3o 

If. 


7306 


7472 


7638 


7804 


7970 


8i35 


166 


262 


83oi 


8467 


8964 


9129 


9295 


9460 


9625 


9791 


i65 


263 


9956 


•121 


•286 


•616 


•781 


•945 


mo 


1275 


1439 


1 65 


264 


421604 


1788 


1033 


1% 

5371 


2261 


2426 


25go 


2754 


2918 


3082 


164 


265 


3246 


3410 


3574 


5?34 


4o65 


4228 


4392 


4555 


4718 


164 


266 


4882 


5o45 


5208 


5697 


586o 


6023 


6186 


6349 


1 63 


267 


65n 


6674 


6836 


6999 


7161 


7324 


7486 


7648 


781 1 


7973 
9591 


162 


268 


8i35 


8297 


li^ 


8621 


8783 


Ifi 


9106 


9268 


9429 


162 


269 


9752 


9914 


•236 


•398 


•720 


•881 


1042 


i203 


161 


270 


43 1 364 


i525 


i685 


1846 


2007 


2167 


2328 


2488 


2649 


2809 


161 


271 


2969 


3i3o 


3290 


3450 


36io 


3770 


3930 
5526 


4090 


4249 


4409 


160 


272 


4569 


4729 


4888 


5048 


5207 


5367 


5685 


5844 


6004 


1 59 


273 


6i63 


6322 


6481 


6640 


6798 
8384 


§s 


7II6 


S?J 


7433 


7592 




274 


7751 


7909 


8067 
9648 


8226 


8701 


9017 


9175 


275 


9333 


9491 


9806 


?S 


•122 


•279 


•437 


•594 


•752 


1 58 


276 


440909 


1066 


1224 


i38i 


1695 


i852 




2166 


2323 


1 57 


277 


2480 


2637 


B 


2950 
45i3 


3io6 


3263 


3419 


3576 


3732 


3889 


.57 


278 


4045 


4201 


4669 


4825 


4981 
6537 


5i37 


5293 


5449 


1 56 


279 


56o4 


5760 


6071 


6226 


6382 


6692 


6848 


7003 


1 55 


N. 





^ 


2 


3 


4 


5 


6 


7 


8 


9 


D. 





A 


TABLE OP 


LOGARITHMS FROM 1 


L TO 


10,000. 


t 


N. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


D. 


280 J447i58 


73i3 


7468 


7623 


7778 


7933 


8088 


8242 


8397 


8552 


1 55 


281 8706 


8861 


90i5 


9170 


9324 


9478 


9633 


9787 


9941 


21 


1 54 


282 :45o249 


o4o3 


0557 


0711 


0865 


1018 


1172 


.326 


.479 


.54 


283 


1786 


1940 


2093 


3247 


2400 


2553 


2706 


2859 


3o.2 


3.65 


1 53 


284 


33i8 


3471 


3624 


3777 


3930 


4082 


4235 


4387 


4540 


4692 


1 53 


285 


4845 


4997 


5i5o 


53o2 


5454 


56o6 


5758 


5910 


6062 


6214 


.52 


286 


6366 


65i8 


6670 


6821 


6973 


8638 


7276 
8789 


7428 


7579 


773. 


1 52 


287 


7882 


8o33 


8184 


8336 


8487 
9995 


8940 


9091 


9242 


.5. 


288 


9392 


9543 


9694 


9845 


•146 


•296 


•447 


•597 


•748 


.5i 


289 


460898 


1048 


1 198 


1348 


1499 


1649 


1799 


1948 


2098 


2248 


i5o 


290 


462398 


2548 


2697 


2847 


2997 


3 146 


3296 


3445 


35o4 
5o85 


3744 


i5o 


291 


3893 


4042 


4191 


4340 


4490 


4639 


4788 


4936 


5234 


149 


292 


5383 


5532 


568o 


5829 


5977 


6126 


6274 
7756 


6423 


6571 


6719 


.49 


293 


6868 


7016 


7164 


73i2 


7460 


7608 


^8^ 


8o52 


8200 


148 


294 


8347 


8495 


8643 


8790 


8938 


9?f^ 


9233 


9527 


9675 


148 


2gD 


9822 


9969 


•116 


•263 


•410 


.557 

2025 


•704 


•85. 


•998 


1.45 


147 


296 


471292 


1438 


1 585 


1732 


1878 


2171 


23.8 


2464 


26.0 


146 


297 


2756 


2903 
4362 


lltl 


3195 
4653 


3341 


3487 


3633 


nil 


538. 


407. 


146 


298 


4216 


4799 
6252 


4944 


5090 


5526 


146 


299 


567. 


58i6 


5962 


6107 


6397 


6542 


6687 


6832 


6976 


145 


3oo 


477121 


7266 


741 1 


8999 


7700 


7844 


7989 


8i33 


8278 


8422 


145 


3oi 


8566 


8711 


8855 


9143 


9287 


9431 


9575 


9719 


9863 


144 


3o2 


480007 


oi5i 


0294 


0438 


o582 


0725 


0869 


.0.2 


..56 


27I? 


144 


3o3 


1443 


1 586 


1729 


1872 


2016 


2159 


2302 


2445 


2588 


143 


3o4 


2874 


3oi6 


3,59 


33o2 


3445 


3587 


3730 


3872 


40.5 


4.57 


143 


3o5 


43oo 


4442 


4585 


4727 


4869 


Son 


5i53 


5295 


5437 


5579 


142 


3o6 


5721 


5863 


6oo5 


6147 


6289 


643o 


6572 


67.4 


6855 


6997 


142 


3o7 


7.38 


7280 


7421 


7563 


7704 


7845 


7986 


8127 


8269 


84.0 


141 


3o8 


855i 


8692 


8833 


lut 


9114 


9255 


9396 


9537 


9677 


98.8 


141 


309 


9958 


••99 


•239 


•520 


•661 


•801 


•941 


io8i 


.222 


140 


3io 


491362 


i5o2 


1642 


1782 


1922 


2062 


2201 


2341 


2481 


2621 


140 


3ii 


2760 


2900 


3o4o 


3.79 


3319 


3458 


IX 


3737 


3876 


40.5 


139 


3l2 


4i55 


4294 


4433 


4572 


4711 


485o 


5.28 


5267 


5406 


139 


3i3 


5544 


5683 


5822 


5960 


?3? 


6238 


6376 


65.5 


6653 


6791 


139 


3i4 


6930 


7068 


7206 


7344 


7621 


7759 


7897 


8o35 


8.73 


.38 


3i5 


83ii 


8448 


8586 


8724 


8862 


8999 


9137 


9275 


9412 


9550 


.38 


3i6 


9687 


9824 


9962 


••99 


•236 


•374 


•5u 


•648 


•785 


•922 


.37 


3i7 


5oio59 


1 196 


1333 


1470 


1607 


1744 


1880 


20.7 


2.54 


229. 
3655 


137 


3i8 


2427 


2564 


2700 


2837 


2973 


3109 


3246 


3382 


35.8 


i36 


3.9 


3791 


3927 


4o63 


4199 


4335 


4471 


4607 


4743 


4878 


5o.4 


i36 


320 


5o5i5o 


5286 


5421 


5557 


5693 


5828 


5964 


6099 


6234 


6370 


.36 


321 


65o5 


6640 


6776 


6911 


7046 


7.81 


7316 


7451 


8934 


772. 


.35 


322 


7856 


7991 


8126 


8260 


8395 


853o 


8664 


8799 


9068 


i35 


323 


9203 


9337 


9471 


9606 


9740 


9874 


•••9 


•.43 


•277 


•4.1 


.34 


324 


5io545 


0679 


o8i3 


0947 


1081 


I2l5 


1 349 


1482 


.6.6 


,750 


.34 


325 


1 883 


2017 


2l5l 


2284 


2418 


255i 


2684 


28.8 


295. 


3o84 


i33 


326 


3218 


335i 


3484 


3617 


3750 


3883 


4016 


4149 


4282 


4414 


.33 


327 


4548 


4681 


48i3 


4946 


5079 


52II 


5344 


5476 


5609 


5741 


i33 


328 


5874 


6006 


6139 


6271 


64o3 


6535 


6668 


6800 


6932 


7064 
8382 


l32 


329 


7.96 


7328 


7460 


7592 


7724 


7855 


7987 


8119 


825i 


l32 


33o 


5i85i4 


8646 


8777 


8909 


9040 


9171 


93o3 


9434 


9566 


9697 


i3i 


33i 


9828 


9959 


••90 


•221 


•353 


•484 


•6i5 


•745 


•876 


.007 


i3i 


332 


52II38 


in 


1400 


i53o 


1661 


1792 


1922 


2o53 


2.83 


23.4 


i3i 


333 


2444 


2705 


2835 


2966 


3o?6 


3226 


3356 


3486 


36.6 


.30 


334 


3746 


3876 


4006 


4i36 


4266 


4396 


4526 


4656 


4785 


49.5 


i3o 


335 


5o45 


5i74 


5304 


5434 


5563 


69^5 


582 2 


595. 


6081 


62.0 


129 


336 


6339 


6469 




6727 


6856 


7114 


7243 


7372 


750. 


129 


337 


763o 


7759 
9045 


8016 


8145 


8274 
9559 


8402 


853 1 


8660 


8788 


'.It 


338 


89.7 


9'74 


9302 


9430 


9687 


98.5 


9943 


••72 


339 


o3o2oo 


o328 


0456 


o584 


0712 


0840 


0968 


1096 


1223 


i35i 


128 


N. 





I 


2 


3 


4 


' 1 


6 


7 


8 


9 


~b7 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



N. 


1 I 


2 


^ 


4 


5 


6 


7 


8 


9 


D. 


340 


531479 


1607 


1734 


1862 


1990 


2117 


2245 


2372 


25oo 


2627 


128 


341 


2754 


2882 


3009 


3i36 


3264 


3391 


35i8 


3645 


3772 


3899 


127 


342 


4026 


41 53 


4280 


4407 


4534 


4661 


4787 


4914 


5o4. 


5167 


127 


343 


5294 


5421 


5547 


5674 
6937 


58oo 


5927 


6o53 


6180 


63o6 


6432 


126 


344 


6558 


66«5 


681 1 


7063 


7189 
8448 


73i5 


7441 


7567 


7693 


126 


345 


7819 


7945 


8071 


8197 


8322 


8574 


8699 


8825 


8931 


126 


346 


9076 


9202 


9327 


9432 


9578 


9703 


9829 


99^4 


••79 


•204 


125 


347 


540329 
1579 


0455 


o58o 


0705 


o83o 


0955 


1080 


1205 


i33o 


J 454 


125 


34S 


1704 


1829 


1953 


2078 


22o3 


2327 


2452 


2576 


2701 


125 


349 


2825 


2950 


3074 


3199 


3323 


3447 


3571 


3696 


3820 


3944 


124 


35o 


544068 


4192 


43i6 


4440 


4564 


4688 


4812 


4936 


5o6o 


5i83 


124 


35i 


5307 


543 1 


5555 


5678 


58o2 


5925 


6049 


6172 


6296 


6419 


124 


352 


6543 


6666 


6789 


6913 


7o36 
8267 


7159 


7282 


74o5 


??g 


7652 


123 


353 


7775 


7898 


8021 


8144 


8389 


85i2 


8635 


8881 


123 


354 


9003 


9126 


9249 
0473 


9371 


9494 


9616 


9739 


9861 


9984 


•106 


123 


355 


55.0228 


o35i 


0595 


0717 


0S40 


0962 


1084 


1206 


1328 


122 


356 


i45o 


1072 


1694 


I8I6 


1938 


2060 


2181 


23o3 


2425 


2547 


122 


357 


2668 


2790 


291 1 


3o33 


3i55 


3276 


3398 


3519 


3640 


3762 


121 


358 


3883 


4004 


4126 


4247 


4368 


4489 


4610 


4731 


4852 


4973 


121 


359 


5094 


52i5 


5336 


5457 


5578 


5699 


5820 


5940 


6061 


6182 


121 


360 


5563o3 


6423 


6544 


6664 


6785 


6905 


7026 


7146 


7267 
8469 


7387 


120 


36i 


7507 


7627 
8829 


7748 


7868 


7988 


8108 


8228 


8349 


8589 


120 


362 


8709 


8948 


9068 


9188 


9308 


9428 


9548 


9667 


9787 


120 


363 


9907 


••26 


•146 


•265 


•385 


•5o4 


•624 


•743 


•863 


•982 


119 


364 


56II0I 


1221 


i34o 


1459 


1578 


I6g8 


18.7 


1936 


2o55 


2174 


119 


365 


2293 


2412 


253i 


2630 


2769 


2887 


3oo6 


3i23 


3244 


3362 


119 


366 


3481 


36oo 


3718 


3837 


3955 


4074 


4192 


43ii 


4429 


4548 


119 


367 


4666 


4784 


4903 


502I 


5.39 


5257 


5376 


5494 


56i2 


5730 


118 


368 


5848 


5966 


6084 


6202 


6320 


6437 


6555 


6673 


6791 


6909 


118 


369 


7026 


7144 


7262 


7379 


7497 


7614 


7732 


7849 


7967 


8084 


118 


370 


568202 


83i9 


8436 


8554 


8671 


8788 


8905 


9023 


9140 


9257 


117 


371 


9374 


9491 


9608 


9723 


9842 


9939 


••76 


•193 


•309 


•426 


117 


372 


570343 


0660 


0776 


0893 


1010 


1 1 26 


1243 


1359 


1476 


1592 


117 


373 


1709 


1825 


1942 


2038 


2174 


2291 


2407 


2523 


2689 


2755 


116 


374 


2872 


2988 


3io4 


3220 


3336 


3452 


3568 


3684 


3800 


39,5 


n6 


375 


4o3i 


4147 


4263 


4379 


4494 


4610 


4726 


4841 


4957 


5072 


116 


376 


5i88 


53o3 


5419 


5534 


565o 


5765 


588o 


5996 


6111 


6226 


u5 


377 


6341 


6457 


6572 


6687 


6802 


6917 


7o32 


7147 


7262 


7377 


ii5 


378 


7492 


7607 


8868 


7836 
8983 


795i 


8066 


81S1 


8295 


8410 


8325 


ii5 


379 


8639 


8754 


9097 


9212 


9326 


9441 


9555 


9669 


114 


380 


579784 


t% 


••12 


•126 


•241 


•355 


•469 


•583 


•697 


•811 


114 


38i 


580925 


ii53 


1267 


i38i 


\U\ 


1608 


1722 


1 836 


1950 


114 


382 


2o63 


2177 


2291 


2404 


25i8 


2745 


2858 


2972 


3o85 


114 


383 


3199 


33i2 


3426 


3539 


3652 


3763 


3879 


3992 


4io5 


4218 


ii3 


384 


433i 


4444 


4557 


4670 


4783 


4896 


5009 


5l22 


5235 


5348 


ii3 


385 


5461 


5574 


5686 


5799 


5912 


6024 


6137 


6250 


6362 


6475 


ii3 


386 


6587 


6700 


6812 


6925 


7037 


7149 
8272 


7262 


7374 
8496 


7486 
8608 


7599 


112 


387 


7711 


7823 
8944 


7935 


8047 


8160 


8384 


8720 


112 


388 


8832 


9o56 


9167 


9279 


9391 


95o3 


96i5 


9726 


9838 


112 


389 


9950 


••6i 


.173 


i284 


•396 


•507 


•619 


•730 


•842 


•953 


112 


390 


591065 


1176 

2288 


1287 


1399 


i5io 


1621 


1732 


1843 


1955 


2066 


III 


391 


2177 


2399 


25io 


2621 


2732 


2843 


2954 


3064 


3i75 


III 


392 


3286 


3397 


35o8 


36i8 


3729 


3840 


3930 


4o6i 




4282 


III 


393 


4393 


45o3 


4614 


4724 


4834 


4945 


5o35 


5i65 


5276 


5386 


IIO 


394 


5496 


56o6 


5717 
6817 


5827 


5937 


6047 


6137 


6267 


6377 


6487 


110 


I'^l 


6597 


6707 


6927 


7037 


7146 


7256 
8353 


7366 


7476 


7586 


IIO 


396 


-,695 
8791 


7805 


79'4 


8024 


8i34 


8243 


8462 


8572 


8681 


IIO 


m 


8900 


9009 


9119 


9228 


9337 


9446 


9556 


9665 


9774 


109 


398 


9883 


9992 


•JOI 


•210 


•319 


•428 


•537 


•646 


•755 


•864 


109 


399 


600973 


10S2 


1191 


1299 


1408 


i5i7 


1625 


1734 


1843 


1951 


109 


N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


"dT 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



N. 





I j 2 


3 


4 


5 


6 


7 


8 


9 


D. 


400 


602060 


l^ \ III] 


2386 


2494 


2603 


2711 


2819 


2928 


3o36 


io3 


401 


3i44 


3469 


3577 
4658 


3686 


3794 


3902 


4010 


4118 


108 


402 


4226 


4334 ! 4442 


455o 


4766 


4874 


4982 


6?66 


5x97 


108 


4o3 


53o5 


54i3 ; 5521 


5628 


IS? 


5844 


5951 


6o5g 


6274 


108 


404 


63Si 


6489 ■ 6396 


6704 


6919 


7026 
8098 


7133 
8203 


7241 


7348 
8419 


107 


4o5 


7455 


7562 1 7669 


7777 


7884 
8954 


7991 


83i2 


107 


406 


8526 


8633 1 8740 


8847 


9061 


9167 


9274 


938 X 


9488 


107 


407 


9394 


9701 1 9808 


9914 


••21 


•128 


•234 


•341 


•447 


•554 


107 


408 


610660 


0767 0873 


0979 


1086 


1192 

2254 


1298 


i4o5 


i5ii 


1617 
2678 


106 


409 


1723 


1829 1936 


2042 


2148 


236o 


2466 


2572 


106 


410 


612784 


2890 2996 


3io2 


3207 


33i3 


3419 


3525 


363o 


3736 


106 


411 


3842 


3947 ' 4o53 


41 59 


4264 


4370 


4475 


4581 


4686 


4792 


106 


412 


4897 


5oo3 ' 5io8 


52i3 


5319 


5424 


5329 


5634 


5740 


5845 


io5 


4i3 


5950 


6o55 j 6160 


6265 


6370 


6476 


658i 


6686 


6790 


6895 


io5 


414 


7000 
8048 


7io5 1 7210 


73i5 


7420 


7325 


2S 


7734 


7839 


7943 
8989 


103 


4i5 


8i53 1 8207 


8362 


8466 


8571 


8780 


8884 


io5 


416 


9093 


9198 


9302 


9406 


95u 


9615 


9719 


9824 


9928 


••32 


104 


417 


620136 


0240 


0344 


0448 


0332 


o656 


0760 


0864 


0968 


1072 


104 


418 


1176 


1280 


1384 


1488 


1592 


1693 


im 


1903 


2007 


2110 


104 


419 


2214 


23i8 


2421 


2523 


2628 


2732 


2939 


3o42 


3146 


104 


420 


623249 


3353 


3456 


3559 


3663 


3766 


3869 


3973 


4076 


4179 


io3 


421 


4282 


4385 


4488 


4391 


4695 


4798 


4901 


5004 


5x07 


5210 


io3 


422 


53i2 


54i5 


53i8 


5621 


5724 


5827 


5929 


6o32 


6x35 


6238 


io3 


423 


6340 


6443 


6546 


6648 


6751 


6853 


6956 


7o58 
8082 


7x61 


7263 
8287 
9308 


io3 


424 


7366 


7468 
8491 


7571 


7673 


7773 


7878 
8900 


7980 


8x85 


102 


423 


8389 


8593 


8695 


8797 


9002 


9104 


9206 


102 


426 


9410 


9512 


9613 


971 5 


9817 


9919 


••21 


•123 


•224 


•326 


102 


427 


630428 


o53o 


o63i 


0733 


0835 


0936 


io38 


1 139 


1241 


i342 


102 


428 


1444 


1545 


1647 


1748 


1849 


1951 


2052 


2i53 


2255 


2356 


lOI 


429 


2457 


2559 


2660 


2761 


2862 


2963 


3064 


3i65 


3266 


3367 


lOI 


430 


633468 


4578 


3670 


3771 


3872 


It 


4074 


4175 


4276 


tilt 


100 


431 


4477 


4679 


4779 


4880 


5o8i 


5x82 


5283 


100 


432 


5484 


55S4 


5683 


5783 


5886 


5986 


6087 


6187 


6287 


6388 


100 


433 


6488 


6588 


6688 


6789 


6889 


6989 


7089 


7.89 
8190 


7290 


It 


100 


434 


7490 


7390 


7690 


7790 


7890 


^^88 


8090 


8290 


99 


435 


8489 


8589 


8689 


8789 


8888 


9088 


9188 


9287 


9387 


99 


436 


94S6 


9586 


9686 


9785 


9885 


9984 


••84 


•i83 


•283 


•382 


99 


437 
438 


640481 


o58i 


0680 


0779 


0879 


0978 


1077 


1177 


1276 
2267 


1375 


99 


1474 


1373 


1672 


1771 


1871 


1970 


2069 
3o58 


2x68 


2366 


99 


439 


2465 


2563 


2662 


2761 


2860 


2959 


3x56 


3235 


3354 


99 


440 


643453 


3551 


365o 


3749 


3847 


3946 


4044 


4143 


4242 


4340 


98 


441 


4439 


4537 


4636 


4734 


4832 


4931 


5029 


5127 


5226 


5324 


98 


442 


542-2 


5521 


5619 


lv,i 


58x5 


59,3 


6011 


6110 


6208 


63o6 


98 


443 


6404 


6302 


6600 


6796 


6894 


6992 


7089 


7187 


7285 


98 


444 


7383 


7481 


7579 


7676 


7774 


7872 


l$t 


8067 


8i65 


8262 


98 


445 


836o 


8458 


8555 


8653 


8750 


8848 


9043 


9140 


9237 


97 


446 


9335 


9432 


953o 


9627 


9724 


9821 


IVl 


••16 


•ix3 


•2x0 


97 


447 


65o3o8 


o4o5 


0502 


0399 


0696 


0793 


0987 


1084 


ix8x 


97 


448 


1278 


1375 


1472 


1569 


1666 


1762 


2826 


1956 


2o53 


2x5o 


97 


449 


2246 


2343 


2440 


2536 


2633 


2730 


2923 


3019 


3xi6 


97 


450 


653213 


3309 


34o5 


35o2 


3598 


3695 


3791 

4754 


3888 


3984 


4080 


96 


45 1 


4177 
5i3S 


4273 


4369 


4465 


4562 


4658 


485o 


4946 


5o42 


96 


452 


.5235 


533 1 


5427 


5523 


56x9 


5715 


58io 


6^64 


6002 


96 


453 


6098 


6194 


6290 


6386 


6482 


6577 


6673 


5?S? 


6960 


96 


454 


70^6 7152 


8202 


7343 


7438 
8393 


7534 


7629 


7820 


7916 
8870 


96 


455 


801 1 1 8107 


8298 


8488 


8584 


8679 


8774 


95 


456 


8965 9060 


9155 


9230 


9346 


9441 


9536 


9631 


9726 


9821 


95 


457 


9916, ••11 


•106 


•201 


•296 


•391 
1339 


•486 


•58i 


•676 


•771 


95 


458 


660865 0960 


io55 


ii5o 


1243 


1434 


i529 
2475 


1623 


1718 


95 


459 


i8i3| 1907 


2002 


2096 


2191 


2286 


238o 


2569 


2663 


Jl 


N. 


1 I 


2 


3 


4 


5 


6 


7 


8 


9 


D. 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


D. 


460 


662753 


2852 


2947 


3o4i 


3i35 


3230 


3324 


34i8 


35i2 


3607 


94 


461 


3701 


3795 


3889 


3983 


4078 


4172 


4266 


436o 


4454 


4548 


94 


462 


4642 


4736 


483o 


4924 
5862 


5oi8 


5lI2 


5206 


5299 


5393 


5487 


94 


463 


558 1 


5675 


5769 


5956 


6o5o 


6143 


6237 


633 1 


6424 


94 


464 


65i8 


6612 


6705 


6799 


6892 


6986 


7079 


7173 


7266 


7360 


94 


465 


8386 


7546 


7640 
8572 


7733 


7826 


7920 


8oi3 


8106 


8.99 


8293 


93 


466 


8479 


8665 


8739 


8852 


8945 


9038 


9i3i 


9224 


93 


% 


9317 


9410 


95o3 


9596 


9689 


97S2 


9875 


9967 


••60 


•I 53 


93 


670246 


0339 


043 1 


o524 


0617 


0710 


0802 


0895 


0988 


1080 


93 


469 


1.73 


1260 


i35S 


i45i 


1 543 


i636 


1728 


1821 


19:3 


2005 


93 


470 


672098 


2190 


2283 


2375 


2467 


2560 


2652 


2744 


2836 


2929 


92 


47 » 


302I 


3u3 


32o5 


3297 


3390 


3482 


3574 


3666 


3708 


385o 


92 


472 


3942 


4o34 


4126 


4218 


43 10 


4402 


4494 


4586 


4677 


4769 


92 


473 


4861 


4953 


5o45 


5i37 


5228 


5320 


54.2 


55o3 


5395 


5687 


92 


474 


5778 


5d7o 


5962 


6o33 


6145 


6236 


6328 


6419 


65ii 


6602 


92 


475 


6694 


6785 


6876 


6968 


7059 


7.5i 


7242 


7333 


7424 
8336 


7516 


91 


476 


g°? 


7698 


7789 


7881 


7972 


8o63 


8i54 


8245 


8427 


91 


477 


8609 


8700 


8791 


8882 


8973 


9064 


9i55 


9246 


9337 


91 


47 rf 


9428 


9519 


9610 


9700 


979' 


9882 


9973 


••63 


•I 54 


•245 


9> 


479 


68o336 


0426 


o5i7 


0607 


0698 


0789 


0879 


0970 


1060 


u5i 


91 


480 


681241 


i332 


1422 


i5i3 


i6o3 


1693 


1784 


1874 


1964 


2o55 


90 


43 1 


2145 


2235 


2326 


2416 


25o6 


2596 


2686 


2777 


2867 


2957 


90 


482 


3 047 


40? 


3227 


3317 


3407 


3497 


3587 


3677 


3767 


3857 


90 


483 


3947 
4845 


4935 


4127 


4217 


4307 


4396 


4486 


4576 


4666 


4756 


90 


484 


0O2D 


5.14 


5204 


5204 


5383 


5473 


5563 


5652 


% 


485 


5742 


5^3 1 


5921 


6010 


6100 


6279 


6368 


6458 


6547 


486 


6636 


6726 


681D 


6904 


6994 


7o83 


7172 


7261 
81 53 


735. 


7440 


89 


487 
488 


7529 
8420 


7618 


7707 


7796 


7886 
8776 


7975 


8064 


8242 


833 1 


89 


85o9 


8098 


8687 


8865 


8953 


9042 


9i3i 


9220 


89 


489 


9309 


9398 


9486 


9575 


9664 


9753 


9841 


9930 


••19 


•107 


89 


490 


690196 


0285 


0373 


0462 


o53o 


0639 


0728 


0816 


0905 


0993 


ll 


491 


loSi 


1170 


1258 


1 347 


1435 


1524 


1612 


2583 


1789 


1877 


492 


1965 


2o53 


2142 


2230 


23i8 


2406 


2494 


2671 


2759 


88 


493 


2847 


2935 
38i5 


3o23 


3iu 


3199 


3287 


3375 
4234 


3463 


355 1 


3639 


88 


494 


3727 


3903 


3991 


4078 


4i66 


4342 


443o 


4517 


88 


495 


46o5 


4693 


4781 


4868 


4936 


5o44 


5i3i 


5219 


5307 


5394 


88 


496 


5482 


5569 


5657 


5744 


5832 


5919 


6007 


6094 


6182 


6269 


87 


4l^ 


6356 


6444 


653 1 


66i8 


6706 


6793 


6880 


6968 


7055 


8014 


87 


7229 
8101 


7317 


7404 


749' 


7578 
8449 


7663 


7752 


7839 


7926 


87 


499 


8i88 


8275 


8362 


8535 


8622 


8709 


8796 


8883 


87 


5oo 


698970 


9057 


9144 


9231 


93.7 


9404 


9491 


9578 


9664 


975i 


87 


5oi 


9«38 


9924 


"ii 


•«98 


•184 


•271 


»358 


•444 


•53 1 


•617 


87 


502 


700704 


0790 


0877 


0963 


io5o 


n36 


1222 


1 309 


1395 

2258 


1482 


86 


5o3 


i568 


i6d4 


1741 


1827 


1913 


1999 


2086 


2172 


2344 


86 


5o4 


243. 


20.7 


26o3 


2689 


2775 


2861 


2947 


3o33 


3ii9 


32o5 


86 


5o5 


329. 


3377 


3463 


3549 


3635 


3721 


38o7 


3893 


3979 


4o65 


86 


5o6 


4i5i 


4236 


4322 


4408 


44q4 


4579 


4665 


4751 


4837 


4922 


86 


507 


5oo8 


5094 


5179 

6o35 


5265 


5350 


5436 


5522 


5607 


5693 


5778 


86 


5o8 


5864 


5949 


6120 


6206 


6291 


6376 


6462 


6547 


663 a 


85 


509 


6718 


6803 


6888 


6974 


7059 


7144 


7229 


73i5 


7400 


7485 


85 


5io 


707570 
8421 


7655 


7740 


7826 


791 1 


7996 


808 1 


8166 


825i 


8336 


85 


5ii 


85o6 


859. 


8676 


8761 


8846 


8931 


9015 


9100 


9185 


85 


5l2 


9270 


9355 


9440 


9524 


S 


9694 


9779 


9863 


9948 


••33 


85 


5i3 


710U7 
0963 


0202 


0287 


0371 


0540 


0625 


0710 


V,% 


0879 


85 


5i4 


1048 


Il32 


1217 


i3oi 


1 385 


1470 


1554 


1723 


84 


5i5 


1807 


2?S 


\l\l 


2060 


2144 


2229 


23i3 


2397 


2481 


2566 


84 


5i6 


265o 


2902 


2986 


3070 


3i54 


3238 


3323 


3407 


84 


^;^ 


3491 


3575 


365, 


3742 


3826 


3910 


4^33 


4078 


4162 


4246 


84 


433o 


4414 


IS? 


458i 


4665 


4749 


4916 


5ooo 


5o84 


84 


519 


5167 


525 1 


5418 


55o2 


5586 


5669 


5753 


5836 


5920 


84 


N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


1)7 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



N. 





I 


2 


3 


4 


5 


' 


7 ' 8 1 9 


D. 1 


520 


716003 


6087 


6170 


6254 


6337 


642! 


65o4 


6588 6671 1 6754 


-^1 


521 


6838 


6921 


7004 


7088 


8oo3 


7254 


7338 


7421 7504 1 7587 
8253 8336 1 8419 


sal 


522 


7671 


7754 


8668 


7920 


8086 


8169 


83: 


523 


85o2 


8585 


8731 


8834 


8917 


9000 


9083 9165 9248 


83 1 


524 


9331 


9414 : 9497 


9380 


9663 


9745 


9828 


9911 9994 ^^77 


83; 


523 


720159 


0242 i 0323 


0407 


0490 


0573 


o655 


0738 0821 \ 0903 


83 i 


526 


09S6 


1068 11 5i 


1233 


i3i6 


1393 


1481 


i5o3 , 1646 i 1728 


82, 


527 


1811 


1893 1 1975 


2038 


2140 


2222 


23o5 


2387 2469 : 2552 


82: 


528 


2634 


2716 


2798 


2881 


2963 


3045 


3127 


3209 


3291 


3374 


82 j 


529 


3456 


3538 


3620 


3702 


3784 


3866 


3948 


4o3o 


4112 


4194 


82 


53o 


724276 


4358 


4440 


4522 


4604 


4685 


4767 


4849 


4931 


5oi3 


82 1 


53 1 


5095 


5.76 , 5258 


5340 


5422 


5303 


5585 


5667 


5748 


583o 


821 


532 


59.2 


5993 ! 6075 


61 56 


6238 


6320 


6401 


6483 


6564 


6646 


82! 


533 


6727 


6S09 1 6890 


6972 


7053 


7'34 


7216 


7297 


7379 
8191 


7460 


81; 


534 


754. 


7623 ' l-joi 


7783 


7866 


7948 


^2'9 


8110 


8273 


81 


535 


8354 


8435 ' 85i6 


8597 


8678 


8739 


8841 


8922 


9003 


9084 


81 


536 


9165 


9246 


9327 


9408 


'4i 


9570 


965i 


9732 


9813 


9893 


81 


537 


9974 


••55 


••36 


•217 


•378 


•459 


•540 1 ^62 1 


•702 


81 


538 


730782 


o863 


0944 


1024 


iio5 


1186 


1266 


i347 i 1428 


i5o8 


81 


539 


\589 


1669 


1730 


i83o 


1911 


1991 


2072 


2l52 ! 2233 


23.3 


81 


540 


732394 


2474 


2555 


2635 


2715 


2796 


2876 


2956 i 3o37 


3117 


80 


54. 


3197 


327S 


3358 


3438 


35i8 


3398 


3679 


3759 3839 


39.9 


80 


542 


3999 


4079 


4160 


4240 


4320 


4400 


4480 


456o 1 4640 


4720 


80 1 


043 


4800 


4bao 


4960 


5o4o 


5l20 


5200 


5279 


5359 ; 5439 


55i9 


80 


544 


5599 


5679 


0739 


5838 


5918 


5998 


6078 


6137 1 6237 


63.7 


80 


545 


6397 


6476 


6556 


6635 


6715 


6795 


6874 


6934 1 7034 


7ii3 


801 


546 


7193 


7272 


l^'z 


7431 


75., 


7390 


7670 
8463 


7749 1 7829 


7908 


791 


547 


79^7 


8067 


8146 


8225 


83o5 


8384 


8343 8622 8701 


iV' 


548 


8781 


8860 


8939 


9018 


9097 


9177 


9256 


9335 


9414 


9493 


79 


549 


9372 


965i 


9731 


9810 


9889 


9968 


••47 


•126 


•2o5 


i284 


79; 


550 


740363 


0442 


0521 


0600 


0678 


0757 


o836 


0915 


0994 


1073 


79! 


55i 


Il52 


i23o 


■i3o9 


i388 


1467 


.546 


1624 


1703 


1782 


i860 


79 


552 


1939 


2018 


2096 


2175 


2234 


2332 


2411 


2489 


2568 


2647 


79 i 

78! 


553 


2725 


2804 28a2 


2961 


3o39 
3823 


3ii8 


3196 


3273 


3353 


343. 


554 


35io 


3588 1 3667 


3745 


3902 


3980 


4038 


4i36 1 42i5 


78 1 


555 


4293 


4371 i 4449 


4328 


4606 


4684 


4762 


4840 


4919 1 4997 


781 


556 


5075 


5i53 1 523i 


5309 


5387 


5465 


5543 t 5621 


5699 1 5777 


78! 


s 


5855 


5933 ! 6011 


6ob9 


6167 


6245 


6323 


6401 


6479 i 6556 


78 


6634 


6712 


6790 


6868 


6945 


7023 


7101 


7179 


7256 7334 
8o33 8110 


78 


559 


7412 


7489 


7307 


7643 


7722 


7800 


7878 


7955 


78 


56o 


748188 


8266 


8343 


8421 


8498 


8576 


8653 1 8731 


8808 1 8885 


77 


56 1 


8963 


9040 


9118 


9193 


9272 


9350 


9427 


9304 


9582 1 9639 


77 i 


562 


9736 


9814 


989. 


9968 


••45 


•123 


•200 


•277 


•354 ! '43 1 


771 


563 


75o5o8 


o586 


0663 


0740 


0817 


0894 


0971 


1048 


II25 j 1202 


771 


564 


1279 


1356 


1433 


i5io 


1 587 


1664 


1741 


1818 


1895 1972 


77 


555 


2048 


2123 : 2202 


2279 


2356 


2433 


2309 2380 


2663 1 2740 


77 1 


566 


2816 


2893 ! 2970 


3o47 


3i23 


3200 


3277 ; 3353 


343o 1 35o6 


77! 


567 


3583 


3660 


3736 


38i3 


3889 


3966 


4042 ! 4119 


4195 1 4272 


77 


568 


4348 


4425 


45oi 


4578 


4654 


4730 


4807 


4883 


4960 5o36 


76 


569 


5lI2 


5189 


5265 


5341 


5417 


5494 


5570 


5646 


5722 I 5799 


76 


570 


755875 
6636 


5951 


6027 1 6io3 


6180 


6256 


6332 


6408 


6484 j 656o 


76 


57. 


6712 6788 1 6864 


6040 


7016 


7092 


7168 


7244 ' 7320 


76 


572 


7396 


7472 1 7548 1 7624 7700 


7775 


785i 


7927 8oo3 i 8070 


761 


573 


8,55 


8230 1 83o6 ' 8382 8458 


8533 


8609 1 8685 : 8761 [ 8836 


76 1 


574 


8912 


8988 1 9063 ! 9139 9214 


9290 


9366 j 9441 1 9517 I 9592 


76 1 


575 


g663 


9743 ' 9819 : 9894 1 9970 


••43 


•121 i ^196 ! '272 ' •3i-i 


75 


576 


760422 


0498 1 0373 j 0649 


0724 


0799 


0875 [ 0950 ! 1025 IIOI 


73 


%l 


1.76 


i25i ■ i326 1402 


1477 


1532 


1627 1702 1 1778 i853 


75 


1928 


2oo3 1 2078 


2i53 


2228 


23o3 


2378 2453 


2529 2604 
3278 3353 


75 


579 


2679 


2754 I 2829 


2904 


2978 


3o53 


3128 32o3 


75 1 


N. 





I j 2 


3 1 4 


5 


6 7 


8 9 


-1 



10 



A TABLE OF LOGARITHMS PROM 1 TO 10,000. 



N. 





■ 1 ' 


3 


1 4 


5 6 


7 


8 


9 


D. 


58o 


76342^ 


35o3 


3578 


3653 


3727 


38o2 


3877 


3952 


4027 


4101 


75 


58i 


Ant 


425i 


4326 


4400 


4475 


455o 


4624 


4699 


4774 


4848 


75 


582 


4923 


499S 


5072 


5.47 


3221 


5296 


5370 


5443 


5320 


5594 


75 


583 


5669 


5743 ! 58i8 


5892 


5966 


6041 


6ll3 


6190 


6264 


6338 


74 


584 


641 3 


6487 6562 


6636 


6710 


6785 


6859 


6933 


7007 


7082 


74 


585 


7i56 


7230 7304 


7379 


7453 


7527 


7601 
8342 


7675 


7749 


7823 
8564 


74 


586 


78y8 

8638 


7972 


8046 


8.20 


8194 


8268 


8416 


8490 


74 


587 


8712 


8786 


8860 


89J4 


9008 


9082 


9i56 


923o 


93o3 


74 


588 


9^77 


945i 


9525 


9599 


9673 


9746 


9820 


9894 


9968 


••42 


74 


589 


770115 


0189 


0263 


o336 


0410 


0484 


0557 


o63i 


0705 


0778 


74 


590 


770852 


0926 


??S 


1073 


1 146 


1220 


1293 


1367 


1440 


i5i4 


74 


59. 


1087 


1661 


1808 


i88i 


1955 


2028 


2.02 


2175 


2248 


73 


592 


2322 


2393 


2468 


2542 


26i5 


2688 


2762 


2835 


2908 


2981 


73 


593 


3o55 


3128 


3201 


3274 


3348 


3421 


3494 


3567 


3640 


3713 


73 


594 


3786 


386o 


3933 


4006 


4079 


4.32 


4223 


4298 


4371 


4444 


73 


595 


4517 


4390 


4663 


4736 


4809 


4882 


4955 


5o28 


5ioo 


5173 


73 


596 


5246 


5319 


5392 


5465 


5538 


56io 


5683 


5756 


5829 


5902 


73 


597 


5974 


6047 


6120 


6193 


6263 


6338 


641 1 


6483 


6556 


6629 


73 


598 


6701 


6774 


6846 


6919 


6992 


7064 


7137 


7209 


7282 


7334 
8079 


73 


599 


7427 


7499 


7572 


7644 


7717 


7789 


7862 


7934 


8006 


72 


600 


778i5i 


8224 


8296 


8368 


844. 


85i3 


8585 


8658 


8730 


8802 


72 


601 


8S74 


8947 


9019 


9091 


9i63 


9236 


9308 


9380 


9432 


9524 


72 


602 


9396 


9669 


9741 


9813 


9885 


9937 


••29 


•lOI 


•.73 


•245 


72 


6o3 


780317 


0389 


0461 


o533 


o6o3 


0677 


0749 


0821 


0893 


0965 


72 


604 


1037 


1109 


ii8i 


1253 


i324 


1396 


1468 


1540 


1612 


1684 


72 


6o5 


1755 


1827 


1899 


1971 


2042 


2114 


2i86 


2258 


2329 


2401 


72 


606 


2473 


2544 


2616 


2688 


2759 


283 1 


S 


2974 


3o46 


3ii7 


72 


607 


3189 


3260 


3332 


3403 


4^89 


3546 


3689 


3761 


3832 


7! 


608 


3904 


3975 


4046 


4118 


4261 


4332 


44o3 


4475 


4546 


7> 


609 


4617 


4689 


4760 


483 1 


4902 


4974 


5o45 


5ii6 


5187 


5259 


71 


610 


785330 


5401 


5472 


5543 


56i5 


5686 


5757 


5828 


5899 


5970 


71 


611 


6041 


6112 


6i83 


6254 


6325 


6396 


6467 


6538 


6609 


6680 


71 


612 


675. 


6822 


6893 


6964 


7035 


7106 


7177 


7248 


7319 


7390 


7' 


6i3 


7460 


IH' 


7602 


7673 


7744 


7815 

8522 


7885 
8593 


7936 


8027 


8098 


71 


614 


8168 


8239 


83io 


838i 


8451 


8663 


8734 


8804 


71 


6i5 


8875 


8946 


9016 


9087 


9157 


9228 


9299 


9369 


9440 


g5io 


7« 


616 


9581 


9631 


9722 


9792 


9863 


9933 


•••4 


0.74 


•144 


•2l5 


70 


617 


790285 


o336 


0426 


0496 


o567 


0637 


0707 


0778 
1480 


0848 


0918 


70 


618 


0988 


1039 


1 1 29 


1199 


1269 


1 340 


1410 


1330 


1620 


70 


619 


1691 


1761 


1 83 1 


1901 


1971 


2041 


2111 


2l8l 


2252 


2322 


70 


620 


792392 


2462 


2532 


2602 


2672 


2742 


2812 


2882 


2952 


3022 


70 


621 


3092 


3i62 


323i 


33oi 


3371 


3441 


33II 


358i 


3631 


3721 


70 


622 


3790 


386o 


3930 


4000 


4070 


4139 


4209 


4279 


4349 


4418 


70 


623 


4488 


4558 


4627 


4697 


4767 


4836 


4906 


4976 


5043 


5ii5 


70 


624 


5i85 


52 34 


5324 


53q3 


5463 


5532 


56o2 


5672 


5741 


58ii 


70 


625 


588o 


5949 


6019 


6088 


6i58 


6227 


6297 


6366 


6436 


65o5 


69 


626 


6574 


6644 


6713 


6782 


6852 


6921 


6990 


7060 


7129 


7198 


69 


627 


7268 


7337 


7406 


7475 
8167 
8858 


7545 


76.4 


7683 
8374 


7752 


7821 


7890 


69 


628 


7960 


8029 




8236 


83o5 


8443 


83i3 


8582 


69 


629 


865i 


8720 


1% 


8927 


8996 


9065 


9134 


9203 


9272 


69 


63o 


799341 


9409 


9478 


9547 


9616 


9685 


9754 


9823 


9892 


9961 


69 


63 1 


800029! 0098 


0167 


0236 


o3o5 


0373 


0442 


031 1 


o38o 


0648 


69 


632 


0717 0786 


o854 


0923 


0992 


io6i 


1129 


1 198 


1266 


1335 


69 


633 


1404I 1472 


i54i 


1609 
2293 


1678 


1747 


i8i5 


1884 


1952 


2021 


69 


634 


2089 2i58 


2226 


2363 


2432 


25oo 


2568 


2637 


2705 


tl 


635 


2774 2842 


2910 


2979 


3047 


3ii6 


3.84 


3252 


3321 


3389 


636 


3457 


3525 


3594 


3662 


3730 


3798 


3867 


3935 
4616 


4oo3 


4071 


68 


til 


4139 


4208 


4276 


4344 


4412 


4480 


4548 


4685 


4753 


68 


482, 


4889 




5o25 


5093 


5i6i 


5229 


5297 


5365 


5433 


68 


639 


55oi 


5569 


5637 


5705 


5773 


5841 


5908 


5976 


6044 


6112 


68 


N. 


I 


2 


3 


4 


5 6 1 


7 


~8~ 


9 


"dT 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



11 



N. 





I 


2 


3 


4 


' 


' 


7 


8 


9 


D. 


"640 


806180 


6248 


63i6 


6384 


645 1 


65i9 


6587 


6655 


6723 


l§ 


68 


641 


6858 


6926 


6994 


7061 


7129 


7197 


7264 


8008 


7400 


68 


642 


7535 


7603 


7670 
8346 


7738 


7806 


7873 


7941 


8076 


68 


643 


8211 


8279 


84.4 


8481 


8549 


8616 


8684 


8731 


8818 


67 


644 


8886 


8953 


9021 


9088 


9i56 


9223 


9290 


9358 


9425 


9492 


67 


645 


9360 


9627 


9694 


9762 


9829 


9896 


9964 


••3 1 


.•98 


•i65 


67 


646 


810233 


o3oo 


0367 


0434 


o5oi 


o569 


0636 


0703 


0770 


0837 


67 


647 


0904 


0971 


,039 


1 106 


1173 


1240 


i307 


1374 


1441 


i5o8 


67 


648 


1575 


1642 


1709 


1776 


1843 


1910 
2579 


1977 


2044 


2111 


2178 


67 


649 


2245 


23l2 


2379 


2445 


25l2 


2646 


2713 


2780 


2847 


67 


65o 


812913 


2980 


3o47 


3X14 


3i8i 


3247 


33i4 


338i 


3448 


35i4 


67 


65i 


358i 


3648 


37.4 


3781 


3848 


3914 


3981 


4048 


4114 


4181 


67 


652 


4248 


43i4 


438 1 


4447 


45i4 


458. 


4647 


47 >4 


4780 


4847 


tl 


653 


49J3 


4980 


5o46 


5ii3 


5179 


5246 


53i2 


5378 


5445 


55ii 


654 


5578 


5644 


5711 


5777 


5843 


59.0 


5976 


6042 


6109 


6.75 


66 


655 


■ 6241 


63o8 


6374 


6440 


65o6 


6373 


6639 


X 


6771 


6838 


66 


656 


6904 


6970 


7o36 


7102 


7169 


7235 


7301 


7433 


8160 


66 


657 


7565 


S292 


8338 


7764 


7830 


& 


7962 


8028 


8094 


66 


658 


8226 


8424 


8490 


8622 


8688 


8754 


8820 


66 


659 


8885 


8951 


9017 


9083 


9149 


92i5 


9281 


9346 


9412 


9478 


66 


660 


819544 


9610 


9676 


9741 


9807 


9873 


& 


•»»4 


••70 


•i36 


66 


661 


820201 


0267 


o333 


0399 


0464 


o53o 


0661 


0727 


0792 


66 


662 


o858 


2233 


0989 


1033 


1120 


1186 


1231 


i3i7 


i382 


1448 


66 


663 


i5i4 


1645 


17IO 

2364 


1775 


1841 


1906 


1972 


2037 


2103 


65 


664 


2168 


2299 
2952 


2430 


2495 


2 560 


2626 


2691 


2756 


65 


665 


2822 


2887 


3oi8 


3o83 


3.48 


32l3 


3279 


3344 


3409 


65 


666 


3474 


3539 


36o5 


3670 


3735 


38oo 


3865 


%: 


3996 


406 1 


65 


667 


4126 


4I9I 


4256 


4321 


4386 


445 1 


45i6 


4646 


47II 


65 


668 


4776 


4841 


4906 
5556 


4971 


5o36 


5ioi 


5i66 


523i 


5296 


536i 


65 


669 


5426 


5491 


5621 


5686 


5751 


58i5 


5S8o 


5945 


6010 


65 


670 


826075 


6140 


6204 


6269 


6334 


6399 


6464 


6528 


6393 


6658 


65 


671 


6723 


6787 


6852 


6917 


6981 


7046 


7111 


7175 


7240 


73o5 


65 


672 
673 


7369 
8oi5 


7434 
-8080 


7495 


7363 


762-8 


.7692.. 


-7-737 


-78.21 


7886 


7951 
8395 


65 
64 


8144 


8209 
8853 


8273 


8338 


8402 


8467 


853 1 


674 


8660 


8724 


8789 


X. 


8982 


9046 


9III 


9175 


9239 


64 


675 


9304 


9368 


9432 


9497 


9625 


9690 


9754 


9818 


9882 


64 


676 


9947 


••n 


••75 


•139 


•204 


•268 


•332 


•396 


•460 


•525 


64 


677 


83o589 


o653 


0717 


0781 


0845 


;s 


0973 


1037 


1102 


n66 


64 


678 


i23o 


1294 


i358 


1422 


i486 


i6i4 


1678 


1742 


1806 


64 


679 


1870 


1934 


1998 


2062 


2126 


2189 


2253 


2317 


238i 


2445 


64 


680 


832509 


2573 


lf,l 


2700 


2764 


2828 


2892 


2956 
3593 


3o2o 


3o83 


64 


681 


3.47 


321 1 


3338 


3402 


3466 


3530 


3657 


3721 


64 


682 


3784 


3848 


39.2 


3975 


4o39 


4io3 


4166 


423o 


4294 


4357 


64 


683 


4421 


4484 


4548 


461 1 


4675 


§?? 


4802 


4866 


4929 
5564 


4993 


64 


684 


5o56 


5l20 


5i83 


5247 


53io 


5437 


55oo 


5627 


63 


685 


5691 


5754 


5817 


588 1 


5944 


6007 


6071 


6i34 


6197 
6830 


6261 


63 


686 


6324 


6387 


6451 


65i4 


6577 


6641 


^]of 


6767 


6894 


63 


687 


8219 


7020 


7083 


7146 


7210 


7273 


7336 


8o3o 


7462 
8093 


7325 


63 


688 


7652 


7715 


ml 


7841 


lit 


7967 


8i56 


63 


689 


8282 


8345 


8471 


8597 


8660 


8723 


8786 


63 


690 


838849 


89.2 


8975 


9o38 


9101 


9164 


$11 


9280 

Hi 


9352 


941 5 


63 


691 


9478 


9541 


9604 


9667 


9729 


9792 


9981 


••43 


63 


692 


840106 


0169 


0232 


0294 


0357 


0420 


0482 


0608 


0671 


63 


693 


0733 


0796 


s 


0921 


0984 
1610 


1046 


1109 


1172 


1234 


1297 


63 


694 


1350 1422 
1985 2047 


1547 


1672 


1735 


1797 


i860 


2347 


63 


695 


2II0 


2172 


2235 


2297 


2360 


2422 


2484 


62 


696 


2609' 2672 
3233 32q5 


2734 


2796 


2859 


2921 
3544 


2983 


3046 


3io8 


3170 


62 


697 
698 


3357 


3420 


3482 


36o6 


3669 


3731 


3793 


62 


3855 


X 


3980 

46oi 


4042 


4104 


4i66 


4229 


4291 


4353 


441 5 


62 


699 


4477 


4664 


4726 


4788 


485o 


4912 


4974 


5o36 


62 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


'K 



12 



A TABLE OF LOGARITHMS FEOM 1 TO 10,000. 



N. 





I 


2 


3 


4 


a 1 6 


7. 


8 


9 


D. 


700 


84509S 


5i6o 


5222 


5284 


5346 


5408 


5470 


5532 


5594 


5656 


62 


701 


5718 


5780 


5842 


5904 


5966 


6028 


6ogo 


6i5i 


62i3 


6275 


62 


702 


6337 


6399 


6461 


6523 


6585 


6646 


6708 
7326 


6770 


6832 


6894 


62 


703 


6955 

7573 
8i8q 


7017 


7079 


7141 


7202 


7264 


7388 


7449 
8066 


75ii 


62 


704 


7634 


& 


7758 


7819 


7881 
8497 


7943 


8004 


8138 


62 


705 


8231 


8374 
8989 


8435 


8559 


8620 


8682 


8743 


62 


706 


88o5 


8866 


.8928 
9542 


905i 


9112 


9174 


9235 


9297 


9358 


61 


Vol 


9419 
85oo33 


9481 


9604 


9665 


9726 


9788 


9849 


991 1 


9972 


6i 


0093 


oi56 


0217 


0279 


o34o 


0401 


0462 


0324 


o585 


61 


709 


0646 


0707 


0769 


o83o 


0891 


0952 


ioi4 


1075 


ii36 


1197 


61 


710 


851258 


l320 


i38i 


1442 


i5o3 


1 564 


1625 


1686 


1747 


1809 


61 


711 


IX 


;g! 


1992 


2o53 


2114 


2175 


2236 


2297 


2358 


2419 


61 


712 


2602 


2663 


2724 


2785 


2846 


2907 


2968 


3029 


61 


7i3 


3090 


3i5o 


32U 


3272 


3333 


3394 


3455 


35.6 


3577 


3637 


61 


714 


3698 


3759 


3820 


388i 


3941 
4549 


4002 


4o63 


4124 


4i85 


4245 


6i 


7i5 


43o6 


4367 


4428 


4488 


4610 


4670 


4731 


4792 


4852 


61 


716 


5l!g 


4974 


5o34 


5095 


5i56 


5216 


5277 


5337 


5398 


5459 


61 


]\l 


5580 


5640 


5701 


5761 
6366 


5822 


5882 


5943 
6548 


6oo3 


6064 


61 


6124 


6i85 


6245 


63o6 


6427 


6487 


6608 


6668 


60 


719 


6729 


6789 


685o 


6910 


6970 


7o3i' 


7091 


7152 


7212 


7272 


60 


720 


857332 


7393 


7453 


75i3 


7^74 


7634 


7694 


If, 


78.5 
9018 


7875 
8477 
9078 


60 


721 


7935 


7995 
8097 


8o56 


8116 


8176 


8236 


8297 


60 


722 


8537 


8657 


8718 


8778 


8838 


8898 


•i58 


60 


723 


9i38 


9198 


9258 


9318 


9370 
9978 


9439 


9499 


9619 


9679 
•278 


60 


724 


9739 
86o338 


9799 


9859 


9918 


••38 


••98 


•218 


60 


725 


0398 


0458 


o3i8 


0578 


0637 


0697 


0757 


0817 


0877 


60 


726 


oq37 


0996 


io56 


1116 


1176 


1236 


1295 


i355 


I4i5 


1475 


60 


727 
728 


1 534 


1594 


1 654 


1714 

23lO 


1773 


i833 


1893 


1952 


2012 


2072 


60 


2l3l 


2191 

2787 


2231 


2370 


243o 


2489 


2549 


2608 


2668 


60 


729 


2728 


2847 


2906 


2966 


3o25 


3o85 


3144 


3204 


3263 


60 


730 


863323 


3382 


3442 


35oi 


356i 


3620 


368o 


3739 


3799 


3858 


59 


73. 


3917 


3977 
4570 


4o36 


4096 


4i55 


4214 


4274 


4333 


4392 


4452 


59 


732 


4DII 


463o 


4689 


4748 


4808 


4867 


4926 


4985 


5o45 


59 


733 


5io4 


5i63 


5222 


5282 


5341 


5400 


5459 


55i9 


5578 


5637 


59 


734 


5696 
6287 


5755 


58i4 


5874 


5933 
6524 


5992 
6583 


6o5i 


6110 


6169 


6228 


59 


735 


6346 


64o5 


6465 


6642 


6701 


6760 


6819 


59 


736 


6878 


6937 
7526 


6996 


7055 


7114 


7173 


7232 


8468 


7350 


?» 


59 


]U 


7467 


7585 
8.74 


7644 
8233 


7703 


7762 


7821 


7939 


59 


8o56 


8ii5 


8292 


83 5o 


8409 


8527 


8586 


59 


739 


8644 


8703 


8762 


8821 


8879 


8938 


8997 


9o56 


9114 


9173 


59 


740 


869232 


9290 


9349 


9408 


9466 


9525 


9584 


9642 


9701 


9760 


59 


741 


9818 


9877 


9935 


9994 


••53 


•ill 


•170 


•228 


•287 


•345 




742 


870404 


0462 


0321 


0579 


0638 


a 


0755 


o8i3 


0872 


:s 


743 


t'3 


1047 


1 106 


1164 


1223 


i339 
ITol 


If, 


1456 


58 


744 


i63i 


1690 


1748 


1806 


1 865 


2040 


?£ 


58 


745 


2i56 


22l5 


2273 


233i 


2389 


2448 


2564 


2622 


58 


746 


2739 


2797 


2855 


2913 


2972 
3553 


3o3o 


3o88 


3.46 


3204 


3262 


58 


?s 


3321 


3379 


3437 
4018 


3495 


36ii 


3669 


2727 


3785 


3844 


58 


3902 


3960 


4076 


4134 


4192 


425o 


43o8 


4366 


4424 


58 


749 


4482 


4540 


4598 


4656 


4714 


4772 


4830 


4888 


4945 


5oo3 


58 


750 


875061 


5iio 
569S 


5i77 


5235 


5293 


535i 


5409 


5466 


5524 


5582 


58 


75i 


5640 


5756 


58i3 


5871 


5929 


5987 


6045 


6102 


6160 


58 


752 


6218 


6276 


6333 


6391 


6449 


65o7 


6564 


6622 


6680 


6737 


58 


753 


6795 


6853 


6910 


6968 


7026 


7083 


7141 


7199 


7256 


7314 


58 


754 


7371 


7429 


7487 


7544 


7602 


7659 


7717 
8292 


7774 


7832 


7889 


58 


755 


8522 


8004 


8062 


8119 


8177 


8234 


8349 


8407 


8464 


57 


756 


8579 


8637 


8694 


8752 
q325 


8809 


8866 


8924 


9^55 


9039 


57 


757 


9096 


9153 


9211 


9268 


9383 


9440 


9497 


96.2 


^■7 


758 


9669 


9726 


9784 


9841 


9898 


& 


••i3 


••70 


•127 j "185 


57 


759 


880242 


0299 


o356 


o4i3 


0471 


o585 


0642 


0699 


0756 


57 


N. 





I 


, I 3 1 


4 


5 6 


7 


8 


9 


D. 



A TABLE OF LOGARITHMS FEOM 1 TO 10,000. 



13 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


D. 


760 


880814 


0871 


0928 


0985 


1042 


1099 


ii56 


I2l3 


1271 


i328 


57 


761 


i385 


1442 


1499 


1 556 


i6i3 


1670 


1727 


1784 


1841 


.898 


57 


762 


1955 


2012 


2069 


2126 


2i83 


2240 


2297 


2354 


2411 


2468 


57 


763 


2325 


258i 


2638 


2695 
3264 


2752 


2809 


2866 


2923 


3548 


3o37 


57 


7^4 


3093 


3i5o 


3207 


3321 


3377 


3434 


3491 
4059 
4625 


36o5 


57 


765 


366 1 


3718 


3775 


3832 


3888 


3945 


4002 


4n5 


4172 


57 


766 


4229 


4285 


4342 


4399 


4455 


4D12 


tu 


4682 


4739 
5303 


57 


]U 


4795 


4852 


4909 


496D 


5022 


5078 


5i92 


5248 


57 


536i 


5418 


5474 


5531 


5587 


5644 


5700 


5757 


58i3 


5870 


57 


769 


5926 


5983 


6039 


6096 


6i52 


6209 


6265 


6321 


6378 


6434 


56 


770 


886491 


6547 


6604 


6660 


6716 


% 


6829 


6885 


6942 


6998 


56 


771 


7034 


71U 


7167 


7223 


7280 


85i6 


7449 


73o5 


736 1 


56 


772 


7617 


7674 


7730 


11% 


7842 


7898 


8011 


8067 


8123 


56 


773 


8179 


8236 


8292 


8404 


8460 


8573 


8629 


8685 


56 


774 


8741 


8797 


8853 


8909 


8965 


9021 


9077 


9134 


9190 


9246 


56 


775 


9302 


9358 


9414 


9470 


9D26 


9582 


9638 


9694 


9730 


9806 


56 


776 


9862 


9918 


9974 


••30 


••86 


•141 


•'97 


•233 




•365 


56 


777 


890421 


0477 


0533 


o589 


0645 


0700 


0756 


0812 


0924 


56 


778 


T, 


io35 


1091 


1 147 
i7o5 


I203 


JS 


i3i4 


1370 


1426 


1482 


56 


779 


1593 


1649 


1760 


1872 


1928 


1983 


2039 


56 


780 


892095 


2i5o 


2206 


2262 


23i7 


2373 


2429 


2484 


2540 


2595 


56 


"^^^ 


265i 


2707 


2762 


2818 


2873 


2929 


3^40 


3o4o 


3096 


3i5i 


56 


782 


3207 


3262 


33i8 


3373 


3429 


3484 


3595 


365i 


3706 


56 


783 


3762 


38i7 


3873 


3928 


3984 


4039 
4593 


4094 


4130 


42o5 


4261 


55 


784 


43i6 


4371 


4427 


4482 


4538 


4648 


4704 


4759 


4814 


55 


■^L^ 


4870 


4925 


4980 


5o36 


5091 


5146 


5201 


5257 


53i2 


5367 


55 


786 


5423 


5478 


5533 


5588 


5644 


ss 


5754 


5809 


5864 


5920 


55 


787 


5975 
6526 


6o3o 


6o85 


6140 


6195 


63o6 


636i 


6416 


6471 


55 


788 


658i 


6636 


6692 


6747 


6802 


6857 


6912 


s 


7022 


55 


789 


7077 


7i32 


7187 


7242 


7297 


7352 


7407 


7462 


7572 


55 


790 


897627 


7682 
823i 


& 


7792 


7847 


7902 


7957 


8012 


t^l 


8122 


55 


791 


8176 


8341 


8396 


8451- 


85o6 


856 1 


8670 


55 


792 


8725 


8780 


8835 


8890 


8944 


8999 


9054 


9109 


9164 


9218 


55 


793 


9273 


9328 


9383 


9437 




9547 


9602 


9656 


971 1 


9766 


55 


794 


9821 


9875 


9930 


9983 


••g4 


0695 


•203 


•258 


•3l2 


55 


795 


900367 


0422 


0476 


o53i 


o586 


0640 


0749 
1295 


0804 


0859 


55 


796 


0913 


°tl 


1022 


1077 


ii3i 


1 186 


1240 


1 349 


1404 


55 


797 


1458 


1 567 


1622 


1676 


1731 


1785 


1840 


1894 


1948 


54 


798 


2oo3 


2057 


2112 


2166 


2221 


2273 


2329 
2873 


2384 


2438 


2492 
3o36 


54 


799 


2547 


2601 


2655 


2710 


2764 


2818 


2927 


2981 


54 


800 


903090 


3 144 


3199 


3253 


3307 


3361 


3416 


3470 


3524 


3578 


54 


80 1 


3633 


3687 


3741 


3795 


3849 


3904 


3958 


4012 


4066 


4120 


54 


802 


4174 


4229 


4283 


4337 


4391 


4443 


4499 


4553 


4607 
5i48 


4661 


54 


8o3 


4716 


4770 


4824 


4878 


4932 


4986 


5o4o 


5094 


5202 


54 


804 


5256 


53io 


5364 


5418 


5472 


5526 


558o 


5634 


5688 


5742 


54 


8o5 


5796 


585o 


5904 


5958 


6012 


6066 


6119 
6658 


6173 


6227 


6281 


54 


806 


6335 


6389 


6443 


6497 


6551 


66o4 


6712 


6766 


6820 


54 


l°l 


6874 


6927 


6981 
7519 


7035 


7089 
7626 


7143 


7196 


7250 


73o4 


7358 


54 


808 


7411 


7465 
8002 


7573 


7680 


7734 


7787 


7841 
8378 


7895 


54 


809 


7949 


8o56 


8110 


8i63 


8217 


8270 


8324 


8431 


54 


8io 


908485 


8539 


8592 


8646 


8699 


8753 


8807 


8860 


8914 


8967 


54 


811 


9021 9074 1 


9128 


9181 


9235 


9289 


9342 


9396 
9930 


9449 


95o3 


^J 


812 


9556 


9610 


9663 


9716 


9770 


9823 


9877 


9984 


••37 


53 


8i3 


910091 


0144 


0197 
0731 


025i 


o3o4 


o358 


041 1 


0464 


03i8 


0571 


53 


814 


0624 


0678 


0784 


o838 


0891 


0944 


Sg 


io5i 


1 104 


53 


8i5 


1.58 


1211 


1264 


.317 


i37i 


1424 


1477 


1 584 


1637 


53 


816 


1690 


1743 


1797 


i85o 


1903 


1956 


2009 


2o63 


2116 


2169 


53 


817 
818 


2222 


2275 


2328 


238i 


2435 


2488 


2541 


2594 


2647 
3178 


2700 


53 


2753 


2806 


2859 


2913 


2966 


3019 


3072 


3i25 


323i 


53 


819 


3284 


3337 


3390 


3443 


3496 


3549 


3602 


3655 


3708 
8 


3761 
9 


53 


N. 


1 I 


2 


3 


4 


5 


6 


7 



14 



A TABLE OF LOGAEITHMS FEOM 1 TO 10,000. 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


D. 


820 


9i38i4 


2^2 


3920 


3973 


4026 


4079 


4i32 


4184 


4237 


4290 


53 


821 


4343 


4449 


45o2 


4555 


4608 


4660 


4713 


4766 


4819 


53 


822 


4872 


4925 


4977 


5o3o 


5o83 


5i36 


5189 


5241 


5294 


5347 


53 


823 


5400 


5453 


55o5 


5558 


56ii 


5664 


5716 


5769 


5822 


5875 


53 


824 


5927 


5980 


6o33 


6o85 


6i38 


6191 


6243 


6296 


6349 


6401 


53 


825 


6434 


65o7 


6559 


6612 


6664 


6717 


6770 


6822 


6875 


6927 


53 


826 


6980 


7033 


708D 


7138 


7190 


7243 


7295 


7348 


7400 


7433 


53 


827 


7D06 


7558 


761 1 


7663 
8188 


7716 


7768 


7820 


gj? 


7925 


85o2 


52 


828 


8o3o 


8o83 


8i35 


8240 


8293 


8345 


8450 


52 


829 


8555 


8607 


8659 


8712 


8764 


8816 


8869 


8921 


8973 


9026 


52 


83o 


919078 


9i3o 


9183 


9235 


9287 


9340 


9392 


9444 


9496 


9549 


52 


83 1 


9601 


9653 


9706 


9758 


9810 


9862 


9914 


9967 


••19 


••71 


52 


832 


920123 


0176 


0228 


0280 


o332 


o384 


0436 


0489 


o54i 


0593 


52 


833 


0645 


a 


0749 


0801 


o853 


0906 


0958 


lOIO 


1062 


1114 


52 


834 


1166 


1270 


l322 


1374 


1426 


1478 


i53o 


i582 


1634 


52 


835 


1686 


1738 


1790 

23lO 


1842 


1894 


1946 


Itil 


2o5o 


2102 


2i54 


52 


836 


2206 


2258 


2362 


2414 


2466 


2570 


2622 


2674 


52 


837 
838 


2725 


2777 


2829 


2881 


2933 


2985 
35o3 


3o37 


3089 


3i4o 


3192 


52 


3244 


3296 


3348 


3399 


345i 


3555 


3607 


3658 


3710 


52 


839 


3762 


38i4 


3865 


3917 


3969 


4021 


4072 


4124 


4176 


4228 


52 


840 


924279 


433 1 


4383 


4434 


4486 


4538 


4589 


4641 


4693 


4744 


52 


841 


479(3 


4848 


s? 


4951 


5oo3 


5o54 


5io6 


5i57 


??;? 


5261 


52 


842 


5312 


5364 


5467 


55i8 


5570 


5621 


5673 


5776 


52 


843 


5828 


5879 


5931 


5982 


6o34 


6o85 


6137 


6188 


6240 


6291 


5i 


844 


6342 


6394 


6445 


6497 


6548 


6600 


665 1 


6702 


6754 


68o5 


5i 


845 


6857 


6908 


6939 


7011 


7062 


7114 


7165 


7216 


7268 


7319 


5i 


846 


7370 


7422 


7473 


7524 


a 


7627 


7678 


7730 


7781 


7832 


5i 


847 


7883 


7935 


7986 


8o37 


8140 


9191 


8242 


8293 


8345 


5i 


84B 


8396 


8447 


8498 


8549 


8601 


8652 


8703 


8754 


88o5 


8857 


5i 


849 


8908 


8959 


9010 


9061 


9U2 


9163 


9215 


9266 


9317 


9368 


5i 


85o 


929419 


9470 


9521 


9572 


9623 


9674 


9725 


9776 


9827 


2S? 


5i 


85i 


9930 


9981 


*<»32 


••83 


•i34 


•i85 


•236 


•287 


•338 


5i 


852 


930440 


0491 


o542 


0592 


0643 


0694 


0745 


0796 


0847 


0898 


5i 


853 


0949 


1000 


io5i 


1102 


ii53 


1204 


1254 


i3o5 


i356 


1407 


5i 


854 


1458 


1 509 


i56o 


1610 


1661 


1712 


1763 


1814 


1 865 


1915 


5i 


855 


1966 


2017 


2068 


2118 


2169 


2220 


2271 


2322 


2372 


2423 


5i 


856 


2474 


2324 


2575 


2626 


2677 


2727 


2778 


2829 

3335 


2879 


2930 


5i 


857 


2981 


3o3i 


3o82 


3i33 


3i83 


3234 


3285 


3386 


3437 


5i 


858 


3487 


3538 


3589 


3639 


3690 


3740 


3791 


3841 


3892 


3943 


5i 


859 


3993 


4044 


4094 


4145 


4195 


4246 


4296 


4347 


4397 


4448 


5i 


860 


934498 


4549 


4599 


4650 


4700 


4751 


4801 


4852 


4902 


4953 


5o 


861 


5oo3 


5o54 


5io4 


5x54 


52o5 


5255 


53o6 


5356 


5406 


5457 


5o 


862 


5507 


5558 


56o8 


5658 


5709 


5759 


5809 


5860 


5910 


5960 


5o 


863 


6011 


606 1 


6111 


6162 


6212 


6262 


63i3 


6363 


6413 


6463 


5o 


864 


6514 


6564 


6614 


6665 


6715 


6765 


68i5 


6865 


6916 


6966 


5o 


865 


7016 


7066 


7117 


7167 


7217 


7267 


7317 


7367 


7418 


7468 


5o 


866 


7518 


7568 


7618 


7668 
8169 


7718 
8219 


lltl 


7819 
8320 


7869 
8370 


7919 


7969 


5o 


867 


8019 


8069 


8119 


8420 


8470 


5o 


868 


8520 


8570 


8620 


8670 


8720 


8770 


8820 


8870 


8920 


8970 


5o 


869 


9020 


9070 


9120 


9170 


9220 


9270 


9320 


9369 


9419 


9469 


5o 


870 


939519 


9569 


9619 


9669 


9719 
0218 


9769 


9819 


9869 


9918 


9968 


5o 


871 


940018 


0068 


ou8 


0168 


0267 


o3i7 


o367 


0417 


0467 


5o 


872 


o5i6 


o566 


0616 


0666 


0716 


0765 


o8i5 


o865 


09.5 


0964 


5o 


873 


I0I4 


1064 


1114 


ii63 


I2l3 


1263 


i3i3 


i362 


1412 


1462 


5o 


874 


i5ii 


i56i 


1611 


1660 


I7I0 


1760 


1809 


1855 


1909 
24o5 


1958 


5o 


875 


2008 


2o58 


2107 


2157 


2207 


2256 


23o6 


2355 


2435 


5o 


876 


25o4 


2554 


2603 


2653 


2702 


2752 


2801 


285i 


3^96 


2950 


5o 


877 


3ooo 


3049 


3593 


3148 


3198 


3247 


3297 


3346 


3445 


59 


878 


3495 


3544 


3643 


s 


3742 


X 


3841 


3890 
4384 


3939 


^ 


879 


3989 


4o38 


4088 


4137 


4236 


4335 


4433 


59 


N. 


1 I 


, i 3 


4 


5 


6 


7 


8 


9 


D. 



A TABLE OF LOGARITHMS FROM 1 TO 10,000. 



15 



N. 





I 


2 


3 


4 


5 


6 


1 7 


8 


9 


D. 


88o 


944483 


4532 


458 1 


463 1 


4680 


4729 


4779 1 4828 


4B77 


4927 


49 


88 1 


4976 


5o25 


3074 


5i24 


5173 


5222 


5272 5321 


5370 


5419 


49 


882 


5469 


55i8 


5567 


56i6 


5665 


5715 


5764 ! 58i3 


5862 


39,2 


49 


883 


5961 


6010 


6039 


6108 


6157 


6207 


6236 


63o3 


6354 


64o3 


49 


884 


6452 


65oi 


655i 


6600 


6649 


6698 


6747 
7238 


6796 


6845 


6^94 


49 


885 


6943 


6992 


7041 


7090 


7140 


7189 


7287 


7336 


7385 


49 


886 


7434 


7483 


7532 
8022 


758i 


763o 


7679 


7728 


7777 


7826 


7875 


■ 49 


887 


7924 


7973 


8070 


8119 


8168 


8217 


8266 


83i5 


8364 


49 


888 


841 3 


8462 


85ii 


856o 


8609 


8657 


8706 


8755 


8804 


8853 


49 


889 


8902 


8951 


8999 


9048 


9097 


9146 


9195 


9244 


9292 


9341 


49 


890 


949390 


9439 


9488 


9536 


9585 


9634 


9683 


973 1 


9780 


9829 


49 


891 


9«7S 


9926 


9975 


••24 


«»»73 


•121 


•170 


•219 


•267 


•3i6 


49 


892 


930365 


0414 


0462 


o5n 


o56o 


0608 


0637 


0706 


0754 


oSo3 


49 


893 


o85i 


0900 


0949 


0997 


1046 


1095 


1143 


1192 


1240 


1289 


49 


894 


i338 


1 386 


1435 


1483 


i532 


1 580 


1629 


1677 


1726 


1773 


ii 


895 


1823 


1872 


1920 


1969 


2017 


2066 


2114 


2i63 


22U 


2260 


896 


23o« 


2356 


2403 


2453 


2502 


255o 


2399 


2647 


2696 


2744 


48 


897 


2792 


2841 


2809 


2938 


2986 


3o34 


3o83 


3i3i 


3i8o 


3228 


48 


898 


3276 


3325 


3373 


3421 


3470 


35i8 


3566 


36i5 


3663 


3711 


48 


899 


3760 


38o8 


3856 


3905 


3953 


4001 


4049 


4098 


4146 


4194 


48 


900 


954243 


4291 


4339 


4387 


4435 


4484 


4532 


438o 


4628 


4677 


48 


901 


4725 


4773 ! 4821 


4869 


4918 


4966 


5oi4 


5o62 


5iio 


3i58 


48 


902 


3207 


5255 I 53o3 


535I 


5399 


5447 


5495 


5543 


5592 


5640 


48 


903 


5688 


5736 


5784 


5832 


5880 


5928 


5976 


6024 


6072 


6120 


48 


904 


6168 


6216 


6265 


63 1 3 


6361 


6409 


6457 


65o5 


6553 


6601 


48 


^05 


6649 


6697 


6745 


6793 


6840 


6888 


6936 


6984 


7032 


7080 


48 


906 


7120 


7176 


7224 


7272 


7320 


7368 


7416 


7464 


75i2 


7539 


48 


907 


^^o"? 


7655 


7703 


775i 
8229 


7799 


7847 


7894 


7942 
8421 


7990 


8o38 


48 


908 


8086 


8i34 


8181 


8277 


8323 


8373 


8468 


8316 


48 


909 


8564 


8612 


8659 


8707 


8755 


88o3 


885o 


8898 


8946 


8994 


48 


910 


959041 


9089 


9137 


9185 


9232 


9280 


9328 


9375 


9423 


9471 


48 


911 


9518 


9566 9614 


9661 


9709 


9737 


9804 


9852 


9900 


9947 


48 


912 


9995 


••42 


••90 


•i38 


•l83 


•233 


•280 


•328 


•376 


•423 


48 


9i3 


960471 


o5i8 


o566 


o6i3 


0661 


0709 


0756 


0804 


o85i 


0899 


48 


914 


0946 


0994 


1 041 


1089 
1 563 


ii36 


ii84 


I23l 


nS 


i326 


1374 


47 


9i5 


1421 


It's 


i5i6 


1611 


1 658 


1706 


1801 


1848 


47 


916 


1895 


1990 


2o38 


2085 


2l32 


2180 


2227 


2275 


2322 


47 


9'7 


2369 


2417 


2464 


25ll 


2559 


2606 


2653 


2701 


2748 


2795 


47 


9.8 


2843 


2890 


2937 


2985 


3o32 


3079 


3i26 


3i74 


3221 


3268 


47 


919 


33i6 


3363 


3410 


3457 


35o4 


3552 


3399 


3646 


3693. 


3741 


47 


920 


963788 


3835 


3882 


3929 


3977 


4024 


4071 


4118 


4i65 


4212 


47 


921 


4260 


4307 


4354 


4401 


4448 


4495 


4542 


4590 


a 


4684 


47 


922 


4731 


4778 


4825 


4872 


4919 


4966 


5oi3 


5o6i 


5i55 


47 


923 


5202 


3249 


5296 


5343 


lu: 


5437 


5484 


553i 


5578 


5625 


47 


924 


5672 


5719 


5766 


58i3 


5907 
6376 


5q34 


6001 


6048 


6095 


47 


923 


6142 


6189 
6658 


6236 


6283 


6329 


6423 


6470 


6317 


6564 


47 


926 


6611 


6705 


6752 


6799 


6845 


6892 


6939 


6986 


7033 


47 


^2^ 


7080 


7127 


7173 


7220 


7267 


73i4 


736i 


7408 


7454 


7301 


47 


7548 


7595 


7642 


7688 


7735 


7782 


7829 


7875 


7922 


& 


47 


929 


8016 


8062 


8109 


8i56 


8203 


8249 


8296 


8343 


8390 


47 


930 


968483 


853o 


8576 


8623 


8670 


8716 


8763 


8810 


8856 


8903 


47 


931 


8950 


8996 


9043 


9090 


9i36 


9i83 


9229 


9276 


9323 


9369 


47 


9? 


9416 


9463 


9309 


9356 


9602 


9649 


9695 


9742 


9789 


9*^35 


47 


933 


9882 


2S 


9973 


••21 


••68 


•ii4 


•161 


•207 


•254 


•3 00 


47 


934 


970347 


0440 


0486 


o533 


0579 


0626 


0672 


;s? 


0765 


46 


93d 


0812 


o858 


0904 


0951 


0997 


1044 


1090 


1137 


1229 


46 


936 


1276 


l322 


1369 


I4i5 


1461 


i5o8 


1 554 


i6oi 


1647 


1693 


46 


$1 


1740 


1786 


i832 


1879 


1925 


1971 


2018 


2064 


2110 


2157 


46 


2203 


2249 


2295 


2342 


2388 


2434 


2481 


2527 


2573 


2619 


46 


939 


2666 


2712 


2758 


2804 


285i 


2897 


2943 


2989 


3o35 


3oS2 


J6 


N. 





I 


2 


3 


4 5 


6 


7 


8 


9 


-1 



16 



A TABLE OP LOGAKITHMS FROM 1 TO 10,000. 



N. 





I 


2 


3 


4 


5 


6 


7 


8 1 9 


D. 


940 


973128 


3174 


3220 


3266 


33i3 


3359 


34o5 


3451 


3497 


3543 


46 


941 


S; 


3636 


3682 


3728 


3774 


3820 


3866 


4374 


39^9 


4oo5 


46 


942 


4097 


4143 


4189 


4235 


4281 


4327 


4420 


4466 


46 


943 


45i2i 4558 


4604 


465o 


4696 
5i56 


4742 


4788 


4834 


4880 


4926 


46 


944 


49721 5oi8 


5o64 


5iio 


5202 


5248 


5294 


5340 


5386 


46 


945 


5432: 5478 


5524 


5570 


56i6 


5662 


5707 


5753 


5799 


5845 


46 


946 


589.: 5937 


5983 


6029 
648a 


6075 


6121 


6167 


6212 


6258 


63o4 


46 


947 


635oi 6396 
680S; 6854 


6442 


6533 


6579 


6625 


6671 


6717 


6763 


46 


948 


6900 


6946 


6992 


7037 


7083 


7129 


7175 


7220 


46 


949 


7266; 7312 


7358 


7403 


7449 


7495 


7541 


7586 


7632 


7678 


46 


950 


977724' 7769 


7815 


7861 


It, 


7952 
8409 


7998 


8043 


8089 


8i35 


46 


95i 


8181 8226 


8272 


83i7 


8454 


85oo 


8546 


8591 


46 


952 


8637! 8683 


8728 


8774 


8819 
9275 


8865 


89.1 


8956 


9002 


9047 


46 


953 


9093 9 1 38 


9184 


9230 


9321 


9366 


9412 


9457 


95o3 


46 


954 


9548 9594 


9639 


9685 1 9730 


9776 


982. 


9867 


99' 2 


9958 


46 


955 


980003 0049 
0458; o5o3 


0094 


0140 oi85 


023 1 


0276 


0322 


0367 


0412 


45 


956 


o549 


0594 0640 


o685 


0730 


0776 


0821 


0867 


45 


957 


0912 0957 


ioo3 


1048 1 1093 


1.39 


1184 


1229 


1275 


l320 


45 


958 


iJyo 1411 


1456 


i5oi 1 i547 


1592 


i637 


1 683 


1728 


1773 


45 


959 


I8I9 1864 


1909 


1934 2000 


2045 


2090 


2i35 


2181 


2226 


45 


960 


982271 : 2310 


2362 


2407 1 2452 


2497 


2543 


2588 


2633 


2678 


45 


961 


2723 2769 


2814 


2859 


2904 


2949 


2994 


3 040 


3o85 


3i3o 


45 


962 


3175; 3220 


3265 


33ro 


3356 


3401 


3446 


3491 


3536 


358i 


45 


963 


3626: 3671 


3716 


3762 


38o7 


3852 


3897 


4392 


3987 


4o32 


45 


964 


40771 4122 


4167 


4212 


4257 


43o2 


4347 


4437 


4482 


45 


965 


4527 4572 


4617 


4662 


4707 


4752 


4797 


4842 


4887 


4932 
5382 


45 


966 


4977 5o22 


5067 


5lI2 


5,57 


5202 


52.17 


5292 


5337 


45 


967 


5426: 5471 


55.6 


5561 


56o6 


5651 


5696 


574. 


5786 


5830 


45 


968 


5875 5920 


5965 


6010 


6o55 


6100 


6144 


6189 


6234 


6279 


45 


969 


6324 6369 


64i3 


6458 


65o3 


6548 


6593 


6637 


6682 


6727 


45 


970 


986772 6817 


686 1 


6906 


6951 


6996 


7040 


7085 


7i3o 


7175 


45 


971 


7219 7264 


8202 


7353 


7398 


7443 


7488 


7532 


7577 


7622 
8068 


45 


972 


7666 77 1 1 


7800 


7845 


f^l 


7934 
838i 


7979 
8425 


8024 


45 


973 


8ii3: 8i57 


8247 


8291 


8470 


85i4 


45 


974 


8559 


8604 


8648 


8693 
9 1 38 


8737 


8782 


8826 


8871 


X 


8960 


45 


975 


9005 


9049 


9094 


9i83 


9227 


9272 


93i6 


94o5 


45 


976 


9450 


9494 


9539 


9583 


9628 


9672 


97'7 


9761 


9806 


9850 


44 


977 
978 


9895 


9939 


9983 


••28 


••72 


•1.7 


•161 


•206 


•25o 


•294 


44 


990339 


o383 


0428 


0472 


o5i6 


o56i 


o6o5 


o65o 


S^ 


0738 


44 


979 


0783 


0827 


0871 


0916 


0960 


1004 


1049 


1093 


1182 


44 


980 


991226 


1270 


i3i5 


1359 


i4o3 


1448 


1492 


1536 


i58o 


1625 


44 


981 


1669 


17.3 


1758 


1802 


1846 


1890 


1935 


'979 


2023 


2067 


44 


982 


2111 2i56 


2200 


2244 


2288 


2333 


2377 


2421 


2465 


25o9 


44 


983 


2554I 2598 


2642 


2686 


2730 


2774 


2S19 


2863 


2907 


3392 
3833 


44 


984 


2995 


3o39 


3o83 


3127 


3n2 


3216 


3260 


3304 


3348 


44 


985 


3436 


3480 


3524 


3568 36i3 


3657 


3701 


3745 


3789 


44 


986 


3877 


3921 


3965 


4009 


4o53 


4097 
4537 


4141 


4i85 


4229 


4273 


44 


987 


43.7 


4361 


44o5 


4449 


4493 


458i 


4625 


4669 


47i3 


44 


988 


4757 


4801 


4845 


4889 


4933 


4977 


5021 


5o65 


5io8 


5i52 


44 


989 


5196 


5240 


5284 


5328 


5372 


5416 


5460 


55o4 


5547 


5591 


44 


990 


995635 


5679 


5723 


5767 


58ii 


5854 


5898 


5942 


5986 


6o3o 


44 


991 


6on4 


6117 


6161 


62o5 


624Q 


6293 


6337 


638o 


6424 


6468 


44 


992 


65i2 


6555 


6599 
7037 


6643 6687 


6731 


6774 


6818 


6862 


6906 


44 


993 


6949 


6993 


7080 i 7124 


7168 


7212 


7255 


7299 


7343 


44 


994 


7386 7430 


7474 


7517 i 756i 


76o5 
8041 


7648 


7692 


7736 


7779 


44 


995 


7823 7867 


7910 


7954 7998 


8o85 


8129 


8172 


8216 


44 


996 


III 


83o3 


8347 


8390 


8434 


8477 


8521 


8564 


8608 


8652 


44 


997 


8739 


8782 


8826 


8869 


8gi3 

9348 


8g56 


9000 


9043 


9087 


44 


998 


oi3i 


9174 


9218 


9261 


93o5 


9392 


9435 


9479 
99'3 


9522 


44 


999 9565 


9609 


9652 


9696 


9739 


9783 


9826 


9870 


9957 


43 


N. 


1 


, 1 3 1 4 


5 


6 


7 


8 


9 


D. 



i TABLE 

OF 

LOGAEITHMIC 
SINES AND TANGENTS 

FOE ETEET 

DEGREE AND MINUTE 
OF THE QUADEANT. 



Eemaek. The minutes in the left-liand column of eacli 
page, increasing downwards, belong to the degrees at the 
top ; and those increasing upwards, in the right-hand column, 
belong to the degrees below. 



18 



(0 DEGEEES.) A TABLE OF LOGAEITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 1 





0-000000 




10-000000 




0-000000 




Infinite. 


60 




6-463726 


5017-17 


000000 


-00 


6-463726 


5017-17 
2934-83 


13-536274 


S 


2 


764756 


2934-85 


000000 


• 00 


764756 


235244 


3 


940847 


2o82-3i 


000000 


■ 00 


940847 


2082-3l 


059153 


s 


4 


7-065786 


i6i5-i7 
i3i9-68 
1115.75 


000000 


.00 


7-065786 


1615.17 


12-934214 
837304 
758122 


5 


162696 


000000 


.00 


162696 


i3io-6o 
1115-78 

852-54 


55 


6 


241877 


9-999999 


•01 


241878 


54 


7 


308824 


966-53 
852-54 


999999 


.01 


308825 


6331^3 


53 


8 


366816 


999999 


•01 


366817 


52 


9 


417968 


762-63 


999999 
999998 


-01 


417970 
463727 


762-63 


582o3o 


5i 


10 


463725 


689-88 


-01 


689-88 


536273 


5o 


II 


7-5o5ii8 


629-81 


9-999998 


• 01 


7-5o5i2o 


629-81 


12.494880 
457091 


s 


12 


542906 


579-36 
536-41 


999997 


.01 


542909 


579-33 


i3 


577668 


999997 
999996 


.01 


577672 


536-42 


422328 


47 


U 


609853 


499-38 


-01 


609857 


499-39 


390143 
36oi8o 


46 


i5 


639816 


467-14 


999996 


-01 


639820 


467-15 


45 


i6 


667845 


438-81 


999995 


-01 


667849 


438-82 


332i5i 


44 


;? 


694173 


4i3-72 


999995 


-01 


694179 


413-73 


3o582i 


43 


718997 


391-35 


999994 


■01 


719004 


391-36 


g??S 


42 


19 


742477 


371-27 


999993 


-01 


742484 


371-28 


41 


20 


764754 


353-15 


999993 


-01 


764761 


351^36 


235239 


40 


21 


'■&i 


336-72 


9-999992 


•01 


7-785951 
8061 55 


336^73 


12-214049 
193845 


39 

38 


22 


321-75 


999991 


-01 


321^76 


23 


825451 


3o8-o5 


999989 


-01 


825460 


3o8-o6 


174540 
i56o56 


37 


24 


843934 


2^3 -S 


-02 


843944 


295-49 


36 


25 


861662 




-02 


861674 


283-90 


138326 


35 


26 


878695 


273-17 
263-23 


999988 


-02 


878708 


273-18 


121292 


34 


S 


895085 


999987 


-02 


895099 


263-25 


104901 


33 


910879 


IS:?? 


999986 


-02 


910894 


254-01 


089106 


32 


29 


Q26119 


999985 


•02 


926134 


245-40 


073866 


3i 


3o 


940842 


237-33 


999983 


-02 


940858 


237-35 


059142 


3o 


3i 


7-955082 


229-80 


9-999982 


'02 


7-955100 


229-81 


12.044900 


It 


32 


968870 


222-73 


999981 


•02 


968889 


222-75 


o3iiii 


33 


982233 


216-08 


999980 


-02 


982253 


2i6-io 


017747 


27 


34 


995198 


209-81 


999979 


-02 


995219 


209-83 
203^92 


004781 


26 


35 


8-007787 


203-90 
198-31 


999977 
999976 


-02 


8-007809 
020045 


11.992191 
979955 
968055 


25 


36 


020021 


-02 


198-33 


24 


37 


031919 

043501 


193-02 
188.01 


999975 


-02 


031945 


103-05 


23 


38 


999973 


-02 


043527 


i88-o3 


956473 


22 


39 


054781 


183-25 


999972 


-02 


054809 


183-27 


945191 


21 


40 


065776 


178.72 


999971 


•02 


o658o6 


178-74 


934194 


20 


41 


8-076500 
086965 


174-41 


"SSS 


-02 


8-076531 


174^44 


11.9234.69 
9i3oo3 


\l 


42 


170-31 


•02 


086997 


170^34 


43 


097183 


166-39 
162-6.5 


999966 


•02 


097217 


166-42 


002783 
892797 
8feo37 


n 


44 


107167 


999964 


•03 


107202 


162^68 


16 


45 


1 16926 


159-08 
155-66 


099963 


•o3 


116963 


159-10 

155-68 


i5 


46 


1 26471 


999961 


•o3 


126010 


873490 


14 


47 
48 


i358io 


152-38 


999959 
999958 


■o3 


i3585i 


i52-4i 


864149 


i3 


144953 


149-24 


•o3 


144Q96 
153952 


149-27 


855004 


12 


49 


153907 


146-22 


999956 


•o3 


146-27 


846048 


II 


5o 


162681 


143-33 


999954 


•o3 


162727 


143-36 


837273 


10 


5i 


8-171280 


140-54 


9-999952 


•03 


8-171328 


140-57 


11.828672 


I 


52 


179713 


137-86 


999950 


-03 


;ss 


;r5:^2 


820237 


53 


187985 


135.29 


999948 


•o3 


811964 
8o3844 


7 


54 


196102 


i32.8o 


999946 


•o3 


196156 


132-84 


6 


55 


204070 


i3o-4i 


999944 


• o3 


204126 


i3o-44 


795874 
788047 


5 


56 


2 1 1895 


128-10 


999942 


•04 


211953 


128-14 


4 


57 


219581 


125-87 


999940 


•04 


219641 


125-90 


?» 


3 


58 


227134 


123-72 


999938 


■04 


227195 


123-76 


2 


59 


234557 


121-64 


999936 


.04 


234621 


121-68 


765379 


I 


60 


241855 


119-63 


999934 


• 04 


241921 


119-67 


758079 







Cosine 


D. 


Sine 




Cotang. 


D. 


Tang. 


mT 



(89 DEGREES.) 



SINES AND TANGENTS. (1 DEGEEE.) 



19 



M. 


Sine 


D 




Cosine 


D. 


Tang. 


D 




Cotang. 







8-241855 


119 


63 


9-999934 


04 


8-241921 


119 


67 


11-758070 


60 


I 


249033 
256094 


117 


68 


999932 


04 


249102 


1x7 


ll 


750898 


tl 


2 


ii5 


80 


999929 


04 


256i65 


ii5 


743835 


3 


263042 


ii3 


98 


999927 


04 


263ii5 


114 


02 


736885 


57 


4 


269881 


112 


21 


999925 


04 


269956 


112 


25 


730044 


56 


5 


276614 
283243 


110 


5o 


999922 


04 


276691 


no 


54 


723309 


55 


6 


108 


83 


999920 


04 


283323 


108 


87 


716677 


54 


7 


289773 


107 


21 


999918 


04 


289856 


107 


26 


710144 


53 


8 


296207 


io5 


65 


999915 


04 


296292 


io5 


70 


703708 


52 


9 


302546 


104 


i3 


9999 '3 


04 


3o2634 


104 


18 


697366 


5i 


10 


308794 


102 


66 


999910 


04 


308884 


102 


70 


691116 


5o 


II 


8-314904 


101 


22 


9-999907 


04 


8-3i5o46 


lOI 


26 


11-684954 
678878 
672886 


S 


12 


321027 


^ 


82 


999905 


04 


321122 


99 


87 


i3 


327016 


47 


999902 
999899 


04 


327114 
333025 


98 


5i 


47 


U 


332924 


97 


14 


o5 


97 


19 


666975 


46 


i5 


338753 


95 


86 


999897 


o5 


338856 


95 


90 


661144 


45 


i6 


344504 


94 


60 


999894 


o5 


344610 


94 


65 


655390 


44 


\l 


35oi8i 


93 


38 


lllIVs 


o5 


350289 
355895 
36i43o 


93 


43 


6497" 


43 


355783 


92 


;? 


o5 


92 


24 


644105 


42 


19 


36i3i5 


?; 


999885 


o5 


§5 


08 


638570 


41 


20 


366777 


90 


999882 


o5 


366895 


95 


633io5 


40 


21 


8-372171 


88 


80 


9.999879 


o5 


8-372292 


88 


85 


11-627708 


ll 


22 


377499 


87 


72 


999876 


o5 


382889 


87 


77 


622378 


23 


382762 


86 


67 


999873 


o5 


86 


72 


617111 


37 


24 


387962 


85 


64 


999870 


o5 


388092 
393234 


85 


70 


611908 


36 


25 


393101 


84 


64 


999867 


o5 


84 


70 


606766 


35 


26 


398179 


83 


66 


999864 


o5 


398315 


83 


71 


601685 


34 


3 


4o3i99 


82 


71 


999861 


o5 


403338 


82 


76 


596662 


33 


4o8i6i 


81 


ll 


999858 


o5 


4o83o4 


81 


82 


591696 


32 


29 


4i3o68 


80 


999854 


o5 


4i32i3 


80 


91 


586787 


3i 


3o 


417919 


79 


96 


999851 


06 


418068 


80 


02 


581932 


3o 


3i 


8-422717 


?? 


2I 


9-999848 


06 


8-422869 
427618 


79 


14 


11-577131 


29 


32 


427462 


999844 


06 


78 


3o 


572382 


28 


33 


432156 


77 


40 


999841 


06 


4323i5 


77 


45 


567685 


2 


34 


436800 


76 


57 


999838 


06 


436962 
441 56o 


76 


63 


563038 


35 


441394 


75 


77 


999834 


06 


75 


83 


558440 


25 


36 


445941 


74 


99 


999831 


06 


446110 


75 


o5 


553890 


24 


37 


450440 


74 


22 


999827 


06 


45o6i3 


74 


28 


549387 


23 


38 


454893 


73 


46 


999823 


06 


455070 


73 


52 


544930 
540319 


22 


39 


459301 


72 


73 


999820 


06 


459481 


72 


79 


21 


40 


463665 


72 


00 


999816 


06 


463849 


72 


06 


536i5i 


20 


41 


8-467985 


71 


29 


9-999812 


06 


8-468172 


71 


35 


11-531828 


;§ 


42 


472263 


70 


60 


999809 


06 


472454 


^ 


66 


527546 


43 


476498 


69 


91 


999805 


06 


485o5o 


f, 


523307 
519108 


17 


44 


480693 


tl 


24 


999801 


06 


U 


16 


45 


484848 


59 


999797 


07 


65 


514950 
5io83o 


i5 


46 


488963 


67 


94 


999793 


07 


489170 
493250 


68 


01 


14 


a 


493040 


67 


3i 


9997^6 


07 


67 


38 


506750 


i3 


497078 


66 


tl 


07 


497293 


66 


76 


502707 


12 


49 


5oio8o 


66 


999782 


07 


501298 
505267 


66 


i5 


498702 


II 


5o 


5o5o45 


65 


48 


999778 


07 


65 


55 


494733 


10 


5i 


'tX 


64 


89 


9-999774 


07 


8-509200 
513098 


64 


96 


1 1 - 490800 
486902 


I 


52 


64 


3i 


& 


07 


64 


39 


53 


516726 


63 


75 


07 


516961 


63 


82 


483o39 


7 


54 


52o55i 


63 


19 


999761 


07 


SSS 


63 


26 


479210 
475414 


6 


55 


524343 


62 


64 


999757 


07 


62 


72 


5 


56 


528102 


62 




999753 


07 


528349 


62 


18 


47i65i 


4 


ll 


531828 


61 


58 


999748 


07 


532080 


61 


65 


467920 


3 


535523 


61 


06 


999744 


07 


535779 


6i 


i3 


464221 


2 


59 


539186 


60 


55 


999740 


07 


54^084 


60 


62 


46o553 


I 


60 


542819 


60-04 


999735 


07 


60-12 


456916 







Cosine 


D. 


Sine 




Cotang. 


D. 


Tang 





16 



(88 DKGREES.) 



20 



(2 DEGEEES.) A TABLE OF LOGAEITHMIC 



M. 


Sine 


D. 


Cosine | 


D. 


Tang. 


D. 


Cotang. 







8-5428I9 


60 -04 


9-999735 


-07 


8-543084 


60-12 


11-456916 


60 


I 


546422 


59-55 


999731 


•07 


550268 


59-62 


453309 


u 


2 


tmii 


59-06 
58-58 


999726 


::i 


59-14 


449732 


3 


999722 


553817 


58-66 


446183 


u 


4 


557054 


58-11 


999717 


.08 


557336 


58-19 
57-73 


442664 


5 


56o54o 


57-65 


999713 


.08 


560828 


439172 


55 


6 


563999 


57-19 


999708 


.08 


564291 


57-27 


54 


I 


567431 


56-74 


999704 


.08 


567727 


56-82 


53 


570836 


56-30 


999699 


•08 


571137 


56-38 


428863 


52 


9 


574214 


55.87 


sa 


-08 


574520 


lit 


425480 


5i 


10 


577566 


55-44 


-08 


577877 


422123 


5o 


II 


8-580892 


55-02 


9-999685 


-08 


8.58i2o8 


55-10 


11-418792 


8 


12 


584193 


54-60 


999680 


-08 


584514 


54-68 


415486 


i3 


587469 


54-19 


999675 


-08 


I'^.lt 


54-27 


4i22o5 


47 


14 


590721 


53-79 


999670 


.08 


53-87 


408949 


46 


i5 


593948 


53-39 


999665 


-08 


594283 


53-47 


4o25o8 


45 


i6 


597152 


53-00 


999660 


-08 


597492 


53-08 


44 


17 


6oo332 


52-61 


999655 


-08 


600677 


52-70 


399323 


43 


18 


603489 
606623 


52-23 


999650 


-08 


6o3839 
606976 


52-32 


396161 


42 


19 


51-86 


999645 


.09 


5i-94 
51.58 


393022 
3^9906 


41 


20 


609734 


5i-49 


999640 


.09 


610094 


40 


21 


8-612823 


51-12 


9-999635 


-09 


8.613189 


51-21 


1 1-38681 1 


39 


22 


615891 
618937 


50-76 


999629 


•09 


616262 


5o-85 


383738 


38 


23 


5o-4i 


999624 


•09 


619313 


5o.5o 


380687 


37 


24 


621962 


5o-o6 


999619 


-09 


622343 


5o-i5 


377657 


36 


25 


624965 


49-72 


999614 


.09 


625352 


49-81 


374648 


35 


26 


627948 


49-38 


999608 


•09 


628340 


49-47 


371660 


34 


11 


63091 1 


49-04 


999603 


.09 


63i3o8 


49-13 
48-80 


368692 


33 


633854 


48-71 


999597 


•09 


634256 


365744 
862816 


32 


29 


636776 


48-39 


^lU 


••09 


637184 


48-48 


3i 


So 


639680 


48-06 


.09 


640093 


48-16 


359907 


3o 


3i 


8-642563 


47-75 


9-999581 


•09 


8.642982 
645853 


47-84 


11-357018 


29 


32 


645428 


47-43 


999575 


.09 


47-53 


354147 


2§ 


33 


648274 


47-12 


999570 


-09 


648704 


47-22 


351296 


27 


34 


65iio2 


46-82 


999564 


.09 


65i537 


46-91 


348463 


26 


35 


653911 


46-52 


999558 


.10 


654352 


46 -6i 


345648 


25 


36 


656702 


46-22 


999553 


.10 


657149 
659928 


46-3i 


342851 


24 


ll 


659475 


45.92 


999547 


• 10 


46-02 


340072 


23 


662230 


45-63 


999341 


.10 


662689 


45-73 


3373.1 


22 


39 


664968 


45.35 


999535 


-10 


665433 


45-44 


334567 


21 


40 


667689 


45-06 


999529 


-10 


668160 


45.26 


331840 


20 


41 


8-670393 


44-79 


9-999524 


-10 


8-670870 


44-88 


11-329130 


ll 


42 


673080 


44-5i 


999518 


-10 


673563 


44-61 


326437 


43 


675751 


44-24 


999512 


-10 


676239 


44-34 


323761 


17 


44 


678405 


43-97 


999506 


-10 


tfs 


44-17 


32II00 


16 


45 


681043 


43.70 


999500 


-10 


43-80 


3 1 8456 


i5 


46 


683665 


43.44 


9994o3 
999487 


-10 


684172 


43-54 


3i5828 


14 


s 


686272 


43-18 


-10 


686784 


43-28 


3i32i6 


i3 


688863 


42.92 
42.67 


999481 


-10 


689381 


43 -o3 


810619 


12 


49 


691438 


999475 


-10 


694029 


42-77 


3o8o37 


11 


5o 


693998 


42.42 


999469 


-10 


42-52 


3o547i 


10 


5i 


8-696543 


42-17 


9-999463 


• 11 


8-697081 


42-28 


"la 


I 


52 


699073 


41-92 


999456 


- 1 1 


699617 


42 -o3 


53 


701589 


41-68 


999450 


-II 


702139 


tit 


297861 


I 


54 


704090 


41-44 


999443 


• 1 1 


704646 


295354 


55 


706577 


41-21 


999437 


-II 


707140 


41-32 


292860 


5 


56 


709049 


40-97 


999431 


- 1 1 


709618 


41-08 


200382 
287917 
285465 


4 


57 


711507 


40-74 
4o-5i 


999424 


- II 


712083 


40.85 


3 


58 


713952 


999418 


-11 


714534 


40.62 


2 


59; 


71,6383 


40.29 


999411 


• 1 1 


716972 


40.40 


283028 


I 


60 


718800 


40.06 


999404 


-11 


719396 


40-17 


280604 







Cosine 


D. 


Sine 




Cotang. 


D. 


Tang. 


M. 



(8Y DEGREES.' 



SINES AND TANGENTS. (3 DEGREES.) 



21 



M. 


Sine 


D. 


Cojiue 


D. 


Tang. 


1 ^- 


1 Cotang. 







8.718800 


40.06 


9-999404 


'^ 


8.719396 


40-17 
39.95 


11-280604 


60 


1 


721204 


39-84 


999398 


• 1 1 


721806 


278.94 


^2 


2 


723595 


39.62 


999391 


.11 


724204 


39-74 


275796 


58 


3 


720972 
728337 


39-41 


999384 


. 1 1 


726588 


39.52 


273412 


57 


4 


nil 


999378 


.11 


728959 


39.30 


271041 


56 


5 


730688 


999371 


11 


73.3.7 


3^:8? 

38.68 


268683 


55 


6 


733027 


38-77 


999364 


.12 


733663 


266337 


54 


I 


735354 


38-57 


999337 


.12 


735996 


264004 


53 


737667 


38-36 


999350 


.12 


7383.7 


38.48 


26.683 


52 


9 


739969 


38-i6 


999343 


•12 


740626 


38.27 


259374 


5i 


10 


742209 


37-96 


999336 


•12 


742922 


33.07 


257078 


5o 


II 


8-744536 


37-76. 


9.999329 


■12 


8.745207 


37.87 


11.254793 


8 


12 


746802 


37-56 


999322 


• 12 


747479 


37-68 


252021 


i3 


749055 


37-37 


9993 1 5 


.12 


749740 


37.49 


250260 


47 


•4 


751297 


37-17 


999308 


■12 


731989 


37-29 


24801 1 


46 


i5 


753528 


36-98 


999301 


•12 


754227 


37.10 


245773 


45 


i6 


755747 


36-79 


999294 
999286 


.12 


756453 


36-92 


243547 


44 


17 


707955 


36-61 


.12 


758668 


36-73 


241332 


43 


i8 


76oi5i 


36-42 


999279 


.12 


760872 


36-55 


239128 


42 


19 


762337 


36-24 


999272 


.12 


763o65 


36-36 


236935 


41 


20 


76451 1 


36 -06 


999265 


.12 


765246 


36-18 


234754 


40 


21 


8-766675 


35-88 


9.999257 


.12 


8-767417 


36-00 


11.232583 


g 


22 


768828 


35-70 


999250 


.13 


769578 


35.83 


23o422 


23 


770970 


35-53 


999242 


.13 


771727 


35.65 


228273 


37 


24 


773I0I 


35-35 


999235 


.i3 


773866 


35.48 


226134 


36 


25 


773223 


35.18 


999227 


•i3 


775995 


35.31 


224oo5 


35 


26 


777333 


35-01 


999220 


.i3 


7781 14 


35.14 


221886 


34 


S 


779434 


34-84 


999212 


.i3 


780222 


Itll 


219778 


33 


78x524 


34-67 


999205 


.13 


782320 


217680 


32 


29 


7836o5 


34-51 


999 '97 


.i3 


784408 


34.64 


. 215592 


3i 


3o 


785675 


34-31 


999189 


.13 


786486 


34-47 


2i35i4 


3o 


3i 


8-787736 


34-18 


9.999181 


.i3 


8-788554 


34-31 


11.211446 


ll 


32 


789787 


34-02 


999174 


.i3 


790613 


34-15 


209387 


33 


791828 


33-86 


999 1 66 


.i3 


792662 


IfM 


207338 


27 


34 


793809 


33-70 


999158 


.i3 


794701 


205299 


26 


35 


793881 


33.54 


999 1 00 


.i3 


796731 


33-68 


203269 
20124a 


25 


36 


797894 


33-39 
33.23 


999142 


.i3 


798702 


33-52 


24 


ll 


&,l 


999134 


.i3 


800763 


33-37 


199237 


23 


33.08 


999126 


.i3 


802765 


33-22 


197235 


22 


39 


803876 


32.93 


0991 18 


.i3 


804758 


33-07 


195242 


21 


40 


8o5802 


32-78 


999"° 


.i3 


806742 


32-92 


193258 


20 


41 


8-807819 


32-63 


9.999102 


.i3 


8-808717 


32-78 


U.191283 
189317 


I^ 


42 


809777 


32.49 


^X 


•14 


810683 


32-62 


43 


811726 


32.34 


■14 


812641 


32-48 


187309 


n 


44 


8i366-r 


32.19 
32-05 


999077 


-14 


814589 


32-33 


185411 


16 


45 


815599 


999069 


-14 


816529 


til 


183471 


i5 


46 


817022 


31.91 


999061 


-14 


818461 


181539 


14 


s 


819436 


31-77 


999053 


-14 


820384 


31-91 


179616 


i3 


821343 


31-63 


999044 


•14 


822298 


31-77 


177702 


12 


i9 


823240 


til 


999036 


-14 


824205 


31-63 


173897 


II 


5o 


825i3o 


999027 


-14 


826103 


3i.5o 


10 


5i 


8-8270II 


31-22 


9.999019 


-14 


8-827992 


31-36 


11.172008 


I 


52 


828884 


3i-o8 


999010 


-14 


829874 


31.23 


170126 


53 


830749 


30.95 


999002 


-14 


831748 


3i.io 


168252 


7 


54 


832607 


30.82 


&l 


-14 


8336i3 


30.96 
30.83 


166387 


6 


55 


834456 


30.69 


-14 


835471 


164529 


5 


56 


836297 


30.56 


998976 


■14 


837321 


30.70 


162679 


4 


ll 


838i3o 


30-43 


998967 


-i5 


839163 


30.57 


160837 


3 


58 


839956 


3o-3o 


998958 


-i5 


840998 


30.45 


159002 


2 


59 


841774 


30.17 


998950 


-i5 


842825 


30-32 


157175 


1 


60 


843585 


30-00 


998941 


-i5 


844644 


30-19 


155356 







Cosine 


D. 


Sine 




Cotang. 


D. 


Tang. 


M. 



22 



(4 DEGEEES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 







8-843585 


3o-o5 


9-998941 


•i5 


8.844644 


30-19 


11-155356 


60 


I 


845387 


29-92 


998932 


.i5 


846455 


30-07 


153545 


^ 


2 


847183 


29-80 


998923 


.i5 


848260 


29-95 


i5i74o 


3 


848971 


29-67 


998914 


.i5 


85oo57 


29-82 


;i§?g 


57 


4 


85o75i 


29-55 


998887 


.i5 


85 1 846 


29-70 


56. 


5 


852525 


29-43 


.i5 


853628 


29-58 


146372 


55 


6 


' 854291 


29-31 


.i5 


855403 


29-46 


144597 


54 


7 


856049 


29-19 


998878 


.i5 


857171 


29-35 


142829 
141068 


53 


8 


857801 


28-^4 


998869 


.i5 


858932 
860686 


29-23 


52 


9 


859546 


998860 


.i5 


29-11 


i393i4 


5i 


10 


861283 


998851 


.i5 


862433 


29-00 


137567 


5o 


II 


8-863014 


28-73 


9-998841 


.15 


8.864173 


28-88 


11.135827 


49 


12 


864738 


28-61 


998832 


.i5 


865906 


28-77 


134094 


48 


i3 


866455 


28 -5o 


998823 


.16 


867632 


28-66 


132368 


47 


U 


868i65 


28-39 
28-28 


998813 


■ 16 


869351 


28-54 


1 30649 


46 


i5 


869868 


998804 


.16 


871064 


28-43 


128936 


45 


i6 


871565 


28-17 


itii 


.16 


872770 


28-32 


127230 


44 


I? 


873255 


28-06 


.16 


874469 


28.21 


125531 


43 


i8 


874938 


27-95 


998776 


.16 


876162 


28-11 


123838 


42 


19 


876615 


27-86 


998766 


.16 


877849 


28-00 


I22l5l 


41 


20 


878285 


27-73 


998757 


.16 


879529 


27-89 


120471 


40 


21 


8-879949 


27-63 


9-998747 


•16 


8.881202 


27-79 


11.118798 


39 
38 


22 


881607 


27.52 


998738 


.16 


882869 


27-68 


ii7i3i 


23 


883258 


27-42 


998728 


•16 


884530 


27-58 


115470 


37 


24 


884903 
886542 


27-31 


998718 


•16 


886 1 85 


27.47 


ii38i5 


36 


25 


27-21 


998708 


.16 


887833 


27.37 


112167 


35 


26 


888.74 


27-11 


?& 


.16 


889476 


27.27 


110524 


34 


27 


889801 


27-00 


.16 


891 11 2 


27-17 


108888 


33 


28 


891421 


26-90 
26-80 


998679 


.16 


892742 


27-07 


107258 


32 


29 


893035 


998669 


•17 


894366 


26-97 
26-87 


105634 


3i 


30 


894643 


26-70 


998659 


•17 


895984 


104016 


3o 


3i 


8-896246 


26-60 


9.998649 


•17 


8-897596 


26-77 


11.102404 


29 


32 


807842 


26-51 


998639 


•17 


899203 


26-67 


100797 


28 


33 


899432 


26-41 


998629 


•17 


900803 


26-58 


099197 


27 


34 


901017 


26-31 


998619 


•17 


902398 


26-48 


097602 


26 


35 


902596 


26-22 


998609 


•17 


905570 


26-38 


096013 


25 


36 


904169 


26-12 


998599 


•17 


26-29 


094430 


24 


ll 


905736 


26-03 


998589 


•17 


907147 


26-20 


092853 


23 


907297 


25-93 


998578 


•17 


908719 
910285 


26-10 


091281 
089715 


22 


39 


908853 


25-84 


998568 


•'7 


26-01 


21 


40 


910404 


25-75 


998558 


•17 


911 846 


25-92 


20 


4i 


"US? 


25-66 


9-998548 


•n 


8-913401 


25-83 


11.086599 


It 


42 


25-56 


998537 


.17 


914951 


25-74 


o85o49 


43 


9l5022 


25-47 


998527 


.17 


916495 
gi8o34 


25-65 


o835o5 


17 


44 


9i655o 


25-38 


998516 


.18 


25-56 


081966 


16 


45 


918073 


25-29 


998506 


.18 


919568 


25-47 


080432 


i5 


46 


919591 


25-20 


998495 
998485 


• 18 


921096 


25-38 


078904 
077381 


14 


47 


921 io3 


25-12 


.18 


922619 


25-30 


i3 


48 


922610 


25 -o3 


998474 


.18 


924136 


25-21 


075864 


12 


49 


924112 


24-94 


998464 


.18 


925649 


25-12 


074351 


II 


5o 


925609 


24-86 


998453 


.18 


927156 


25-03 


072844 


10 


5i 


8-927100 


24-77 


9-998442 


• 18 


8-928658 


24-95 


11-071342 


t 


52 


928587 


24-69 


998431 


.18 


93oi55 


24-86 


069845 
068353 


53 


930068 


24-60 


998421 


• 18 


931647 


24-78 


I 


54 


93 1 544 


24-52 


998410 


.18 


933 1 34 


24.70 


066866 


55 


93301 5 


24-43 


998388 


.18 


934616 


24-61 


065384 


5 


56 


934481 


24-35 


.18 


936og3 


24-53 


063907 


4 


57 


935942 


24-27 


998377 


.18 


937565 


24-45 


062435 


3 


58 


937398 


24-19 


998366 


.18 


939032 


24-37 


060968 
059506 
o58o48 


2 


59 


938850 


24-11 


998355 


.18 


94o4q4 


24-30 


I 


60 


940296 


24- o3 


998344 


.18 


941932 


24-21 





1 Cosine 


D. 


Sine 




Cotang. 


D. 


Tang. 1 


"mT 



(85 DEGREES.) 



SINES AND TANGENTS. (5 DEGREE.) 



23 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 







8-940296 
941738 


24-o3 


9-998344 


19 


8-941952 


24-21 


II -058048 


60 




23 


94 


998333 


'9 


943404 


24 


i3- 


056596 


S 


2 


943174 


23 


87 


998322 


19 


944852 


24 


o5 


o55i48 


3 


944606 


23 


79 


998311 


19 


946295 
947734 


23 


97 


053705 


57 


4 


946034 


23 


7' 


998300 


19 


23 


^2 


052266 


56 


5 


947456 


23 


63 


998289 


19 


949168 


23 


o5o832 


55 


6 


948874 


23 


55 


998277 


19 


950597 


23 


-i 


049403 


54 


7 


950287 


23 


48 


998266 


19 


952021 


23 


66 


047979 
046559 


53 


8 


951696 


23 


40 


998255 


19 


953441 


23 


60 


52 


9 


953100 


23 


32 


998243 


19 


954856 


23 


5i 


045144 


5i 


10 


954499 


23 


25 


998232 


19 


956267 


23 


44 


043733 


5o 


II 


8.955894 


23 


17 


9.998220 


19 


8-957674 


23 


37 


11-042326 


8 


12 


957284 


23 


10 


998209 


19 


959075 


23 


It 


040925 
039527 


i3 


958670 


23 


02 


??^1S 


19 


960473 


23 


47 


U 


960052 


22 


t 


19 


961866 


23 


14 


o38i34 


46 


i5 


961429 


22 


998174 


19 


963255 


23 


07 


036745 


45 


i6 


962801 


22 


80 


998163 


19 


964639 


23 


00 


o3536i 


44 


'7 


964170 


22 


73 


998151 


19 


966019 


22 


g 


033981 


43 


18 


965534 


22 


66 


998139 
998128 


20 


968766 


22 


032606 


42 


19 


966893 


22 


59 


20 


22 


79 


o3i234 


41 


20 


968249 


22 


52 


9981 16 


20 


970133 


22 


71 


029867 


40 


2l 


8-969600 


22 


44 


9-998104 


20 


8-971496 


22 


65 


ii-o285o4 


S 


22 


970947 


22 


38 


998092 
998080 


20 


972855 


22 


57 


027145 


23 


972289 


22 


3i 


20 


974209 


22 


5i 


025791 


ll 


24 


973628 


22 


24 


998068 


20 


975560 


22 


44 


024440 


25 


974962 


22 


17 


998056 


20 


976906 


22 


37 


023094 
021752 


35 


26 


976293 


22 


10 


998044 


20 


978248 


22 


3o 


34 


11 


977619 


22 


o3 


998032 


20 


979586 


22 


23 


020414 


33 


978941 


21 


97 


998020 


20 


980921 


22 


17 


019079 


32 


?9 


» 


21 


23 


998008 


20 


982251 


22 


10 


017749 
016423 


3i 


3o 


21 


997996 


20 


983577 


22 


04 


3o 


3i 


8-982883 


21 


77 


9-997985 


20 


8-984899 


21 


97 


ii-oi5ioi 


ll 


32 


984189 


21 


70 


997972 


20 


986217 


21 




013783 


33 


985491 


21 


63 


997959 


20 


988842 


21 


84 


012468 


ll 


34 


ISI 


21 


57 


^]IU 


20 


21 


78 


0IU58 


35 


21 


5o 


21 


990149 


21 


71 


00985 I 
008549 


25 


36 


989374 


21 


44 


997922 


21 


991451 


21 


65 


24 


ll 


990660 


21 


38 


997910 1 

997807 

997885 


21 


992750 


21 


58 


007250 
005955 


23 


991943 


21 


3i 


21 


994045 


21 


52 


22 


39 


993222 


21 


25 


21 


995337 


21 


46 


004663 


21 


4o 


994497 


21 


19 


997872 


21 


996624 


21 


40 


003376 


20 


41 


8.995768 


21 


12 


9-997860 


21 


8.997908 


21 


34 


11-002092 


:? 


42 


997036 
998299 


21 


06 


V,]IU 


21 


999188 


21 


27 


000812 


43 


21 


00 


21 


9-000465 


21 


21 


10-999535 


17 


44 


999560 


20 


q4 


997822 


21 


001738 


21 


i5 


998262 


16 


45 


9-000816 


20 


87 


997809 


21 


oo3oo7 


21 


S 


996993 


i5 


46 


002069 


20 


82 


997797 
997784 


21 


004272 


21 


995728 


14 


47 


oo33i8 


20 


76 


21 


005534 


20 


97 


994466 


i3 


48 


004563 


20 


70 


997771 


21 


006792 


20 


§5 


993208 


12 


49 


oo58o5 


20 


64 


997758 


21 


008047 
009298 


20 


991953 


II 


5o 


007044 


20 


58 


997745 


21 


20 


80 


990702 


10 


5i 


9-008278 


20 


52 


9-997732 


21 


9-010546 


20 


74 


10-989454 
988210 


I 


52 


oogSio 


20 


46 


997719 


21 


oAir, 


20 


68 


53 


010737 


20 


40 


997706 


21 


20 


62 


986969 


I 


54 


01196a 


20 


34 


997680 


22 


014268 


20 


56 


985732 


55 


oi3i82 


20 


29 


22 


oi55o2 


20 


5i 


984498 


5 


56 


014400 


20 


23 


997667 


22 


016732 


20 


45 


983268 


4 


a 


oi56i3 


20 


17 


997654 


22 


017959 


20 


40 


982041 


3 


016824 


20 


12 


■ 997641 


22 


019183 


20 


33 


980817 


2 


59 


oi8o3i 


20 


06 


997628 


22 


o2o4o3 


20 


28 


l]& 


I 


60 


019235 


20-00 


997614 


22 


021620 


20-23 







Cosine 


D. 


Sine 1 




Cotanff. 


D. 


Tang. 



(84 DEGREES.) 



24 



(6 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 







9-019235 


20-00 


9-997614 


.22 


9-021620 


20-23 


10-978880 


60 


I 


020435 


19-95 
19-89 


997601 


.22 


022884 


20.17 


977166 


ll 


2 


02i632 


997588 


.22 


024044 


20.11 


975956 


3 


022825 


19-84 


997574 


•22 


025231 


20-06 


& 


57 


4 


024016 


19-78 


997561 


.22 


026455 


20-00 


56 


5 


025203 


19-78 


997547 


.22 


027655 

028852 


19-95 


972845 


55 


6 


026386 


19-67 


997534 


.23 


;?:§? 


971148 


54 


7 


027567 


19-62 


997520 


.28 


080046 


968763 


53 


8 


028744 


19-57 


997507 


.23 


081287 


19-79 


52 


9 


029918 


i9-5i 


997498 
997480 


• 28 


082423 


19-74 


967575 


5i 


10 


081089 


19-47 


-23 


088609 


19-69 


966891 


5o 


u 


9-o32257 


19-41 


9-997466 


-28 


9-084791 


19-64 


10-965209 


s 


12 


o3342i 


19-86 


997432 


-23 


035969 


19-58 


964081 


i3 


034582 


19-30 


997489 
997425 


-23 


087144 


19-53 


962856 


47 


U 


035741 


19-25 


-23 


088816 


19-48 


961684 


46 


i5 


086896 


19-20 


99741 1 


-23 


089485 


19-48 


9605 1 5 


45 


i6 


088048 


I9-I5 


997897 


-23 


04065 1 


19-38 


959349 


44 


17 


089197 


19-10 


997888 


-23 


04i8i3 


19-33 


■958187 


43 


i8 


040842 


19-05 


& 


-23 


042978 


19-28 


» 


42 


19 


041485 


18.99 


-28 


044180 


19-23 


41 


20 


042625 


18-94 


997341 


-28 


045284 


19-18 


954716 


40 


21 


9-048762 


18.89 


9-997827 


•24 


9-046434 


19-13 


10-953566 


U 


22 


044895 


18-84 


997818 


• 24 


047582 
048727 


19-08 


952418 


23 


046026 


18-79 


», 


•24 


19-08 


951273 


37 


24 


047154 


18-75 


•24 


049869 
o5ioo8 


18-98 


9501 3 1 


36 


25 


048279 


18-70 


997271 


■24 


18-98 
18.89 


?g§S 


35 


26 


049400 


i8-65 


997257 


-24 


o52i44 


34 


S 


o5o5i9 
o5i635 


18-60 


997242 


-24 


058277 


18.84 


946728 


33 


18-55 


997228 


-24 


054407 


18-79 


32 


29 


052749 


i8-5o 


997214 


•24 


055535 


18-74 


944465 


3i 


So 


053859 


18-45 


997199 


-24 


056659 


18-70 


943341 


3o 


3 1 


9-054966 


18-41 


9-997185 


-24 


9-057781 


18-65 


10.942219 


3 


32 


056071 


i8-36 


997170 


-24 


058900 


18-69 


941100 


33 


057172 


i8-3i 


997156 


•24 


060016 


18-55 


989984 
988870 


27 


34 


058271 


18-27 


997141 


•24 


061180 


18.51 


36 


35 


059867 


18-22 


997127 


•24 


062240 


18.46 


987760 


25 


36 


060460 


18-17 


997112 


•24 


063348 


18.42 


986652 


24 


13 


o6i55i 


i8-i3 


997098 


•24 


064453 


18.37 


935547 


33 


062689 


18-08 


997088 


.25 


065556 


18.33 


934444 


22 


39 


068724 
064806 


i8-o4- 


997068 


.25 


066655 


18.28 


933345 


21 


40 


17.99 


997053 


.25 


067752 


18.24 


982248 


20 


41 


9-065885 


17-94 


9.997089 


.25 


9-068846 


18.19 
18. i5 


10.981154 


^9 


42 


066962 


17.90 


997024 


.25 


069988 


980062 


18 


43 


068086 


17.86 


997009 


.25 


071027 


18-10 


928073 
927887 


«7 


44 


069107 


17.81 


996994 


.25 


072118 


18-06 


16 


45 


070176 


17.77 


996979 


.25 


078197 


18-02 


926808 


i5 


46 


071242 


17.72 


996964 


■25 


074278 


17-97 


925722 


14 


s 


072806 


17-68 


996949 


.25 


075356 


17-03 


924644 


i3 


078866 


17-63 


996984 


.25 


076482 


17-89 


923568 


12 


49 


074424 


\llt 


996919 


.25 


o775o5 


17-84 


922495 


1 1 


5o 


075480 


996904 


.25 


078576 


17-80 


921424 


10 


5i 


9-076533 


17.50 


9.996889 


.25 


9-079644 


17-76 


10-920356 


? 


52 


077588 
078681 


17-46 


996874 


.25 


080710 


17-72 


919290 


53 


17-42 


996858 


.25 


081778 


17-67 


918227 


7 


54 


079676 
080719 


17-38 


996843 


.25 


082888 


17-63 


917167 


6 


55 


17.33 


996828 


.25 


088891 


17-59 


916109 


5 


56 


081759 


17.20 
17-25 


996812 


.26 


084947 


17-55 


9i5o53 


4 


ll 


IMI 


996707 


.26 


086000 


17-5. 


914000 


3 


17.21 


996782 


.26 


087050 


17-47 


912950 


2 


59 


084864 


\IM 


996766 


.26 


088098 


17-43 


IVolll 


I 


60 


085894 


996751 


.26 


089144 


17-38 







Cosine 


D. 


Sine 




Cotang. 


D. 


Tang. 


'm7\ 



(83 DEGREES.) 



SINES AND TANGENTS. (7 DEGREES.) 



25 



M. 


Sine 


D. 


Cosme 


D. 


Tang. 


D. 


Cotang. 







9-085894 


17.13 


9-996751 


• 26 


9-089144 


17-38 


10.910856 


60 


I 


086922 


17-09 


996735 


-26 


090187 
091228 


17 


-34 


9008.3 

908772 


It 


2 


087947 


17-04 


996720 


.26 


17 


-3o 


3 


088970 


17-00 


996704 


.26 


092266 


17 


•27 


907734 


57 


4 


089990 


16-96 


996688 


.26 


093302 


17 


-22 


906698 


56 


5 


091008 


16-92 
i6-88 
16.84 


996673 


.26 


094336 


17 


:;? 


905664 


55 


6 

7 


092024 
093037 


996657 
996641 


• 26 
.26 


& 


17 
17 


904633 
9o36o5 


54 
53 


8 


094047 


16-80 


996625 


.26 


097422 
098446 


17 


•3 


902578 


52 


9 


095o56 


16-76 


996610 


.26 


17 


901554 


5i 


10 


096062 


16-73 


996594 


.26 


099468 


16 


•99 


900532 


5o 


II 


9-097065 


16-68 


9-996578 


-27 


9-100487 


16 


95 


"•1« 


ii 


12 


098066 


16-65 


996562 


-27 


101 5o4 


16 


^7 


i3 


099065 


16-61 


996546 


.27 


I025i9 


16 


897481 


S 


U 


100062 


16-57 


996530 


■27 


103532 


16 


84 


896468 


i5 


ioio56 


16.53 


996514 


.27 


104542 


16 


80 


895458 


45 


i6 


102048 


16-49 


996498 


.27 


io555o 


16 


76 


894450 


44 


:i 


io3o37 


16-45 


996482 


.27 


106556 


16 


72 


893444 


43 


io4o25 


16-41 


996465 


•27 


107559 


16 


s 


892441 


42 


•9 


io5oio 


16-38 


l& 


•27 


io856o 


16 


891440 


4x 


20 


105992 


16-34 


■27 


109559 


16 


61 


890441 


40 


21 


9-106973 


i6-3o 


9-996417 


■27 


9-110556 


16 


58 


10-889444 
888449 


39 
38 


22 


107901 


16-27 


996400 


■27 


iii55i 


16 


54 


23 


108927 


16-23 


996384 


•27 


112543 


16 


5o 


887457 


37 


24 


I 0900 I 

1 10873 


16-19 
16-16 


996368 


•27 


II3533 


16 


46 


886467 


36 


25 


996351 


•27 


1 1452 1 


16 


43 


884493 


35 


26 


11.842 


16-12 


996335 


•27 


ii55o7 


16 


S 


34 


27 


II 2809 


16-08 


996318 


•27 


116491 


16 


883500 
882528 


33 


28 


113774 


i6-o5 


996302 


.28 


117472 


16 


32 


32 


29 


1 14737 


16-01 


996285 


.28 


1 1 8452 


16 


ll 


881548 


3i 


3o 


115698 


15-97 


996269 


.28 


119429 


16 


880571 


3o 


3i 


9-116656 


15-94 


9-996252 


.28 


9-120404 


16 


22 


10-879596 
878623 


ll 


32 


117613 


ti; 


996235 


.28 


122348 


16 


18 


33 


1 18567 


996219 


.28 


16 


i5 


877652 


27 


34 


1 19319 


15-83 


996202 


.28 


I233I7 


16 


1 1 


876683 ' 26 


35 


120469 


i5-8o 


996185 


.28 


124284 


16 


07 


875716 ! 25 


36 


121417 


15-76 


996168 


.28 


125249 


16 


04 


874751 ^ 24 


ll 


122362 


15-73 


996151 


.28 


126211 


16 


01 


873789 I 23 

872828 : 22 


i233o6 


15-69 


996134 


.28 


127172 
i28i3o 


i5 


97 


39 


124248 


15.66 


996117 


.28 


i5 


94 


871870 1 21 


40 


125187 


15-62 


996100 


.28 


129087 


i5 


91 


870913 


20 


41 


9-126125 


\tu 


9-996083 


•29 


9-130041 


i5 


87 


10.869959 


;? 


42 


127060 


996066 


•29 


i3o994 


i5 


84 


869006 


43 


127993 


i5-52 


996049 


■29 


131944 


i5 


81 


868o56 


17 
16 


44 


128925 


\l:il 


996032 


•29 


132893 
133839 


i5 


77 


867107 


45 


129854 


996015 


•29 


i5 


74 


866161 


i5 


46 


130781 


15-42 


& 


•29 


134784 


i5 


71 


865216 


14 


47 


131706 


;l:S 


•29 


135726 


i5 


67 


864274 


i3 


48 


i3263o 


995963 


•29 


136667 


i5 


64 


863333 


12 


49 


i3355i 


i5-32 


995946 


■29 


137605 


i5 


61 


862395 
861458 


II 


5o 


134470 


15.29 


995928 


•29 


138542 


i5- 


58 


10 


5i 


9-135387 


15.25 


9-995911 


•29 


9-139476 


i5- 


55 


io.86o524 


I 


52 


i363o3 


l5.22 


995894 


•29 


140409 


i5- 


5i 


i& 


53 


137216 


15.19 


995876 


.29 


i4i34o 


i5- 


48 


1 
6 


54 


i38i28 


i5.i6 


995859 


• 29 


142269 


i5- 


45 


85773. 


55 


139037 


I5.I2 


995841 


•29 


143196 


i5- 


42 


856804 


5 


56 


139944 
i4o85o 


15.09 


995823 


•29 


144121 


i5- 


ll 


855879 


4 


u 


i5.o6 


995806 


-29 


145044 


i5- 


854956 


3 


141754 


i5-o3 


995788 


-29 


145966 


i5- 


32 


854034 


2 


59 


142655 


i5-oo 


995771 


•29 


146885 


i5- 


29 


853ii5 


I 


60 


143555 


14-96 


995753 


•29 


147803 


i5-26 


852197 







Cosine 


D. 


Fine 1 


1 


Cotang. ! 


D. 1 


Tang. M. j 



26 



(8 DEGREES.) A TABLE OF LOGAEITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


T>. 


Cotang. 







9.143555 


14-96 


9-995753 


■3o 


9-147803 


i5-26 


10-852197 


60 


I 


144453 


14-93 


995735 


-3o 


148718 


i5 


23 


85x282 


li 


2 


145349 


14-90 
14-87 


995717 


-3o 


149632 


i5 


20 


85o368 


3 


146243 


995699 


-3o 


i5o544 


i5 


17 


840456 


57 


4 


i47i36 


14-84 


995681 


-3o 


i5i454 


i5 


14 


848546 


56 


5 


148026 


14-81 


995664 


-3o 


152363 


i5 


II 


847637 


55 


6 


149802 


14-78 


995646 


-3o 


153269 


i5 


08 


846731 


54 


7 


14-75 


995628 


-3o 


154174 


i5 


o5 


845826 


53 


8 


i5o686 


14-72 


995610 


•3o 


155077 


i5 


02 


844923 


52 


9 


i5i569 


14-69 


^9559. 


-3o 


155978 


14 


11 


844022 


5i 


lo 


i5245i 


14-66 


995573 


•3o 


156877 


14 


843123 


5o 


II 


9-153330 


14-63 


9-995555 


-3o 


9-157775 


14 


93 


10-842225 


8 


12 


1 54208 


14-60 


995537 


-3o 


158671 


14 


^7 


841329 
840435 


i3 


i55o83 


14-57 


995519 


-3o 


159565 


14 


47 


U 


;g?s 


14-54 


995501 


-3i 


160457 


14 


84 


839543 
838653 


46 


i5 


14-51 


995482 


-3i 


i6i347 


14 


81 


45 


i6 


157700 


14-48 


995464 


-3i 


162236 


14 


79 


i^r. 


44 


I? 


158569 
159435 


14-45 


995446 


-3i 


i63i23 


14 


76 


43 


i8 


14-42 


995427 


-3i 


164008 


14 


73 


835992 


42 


19 


i6o3oi 


14-39 
14-36 


995409 


-3i 


164892 


14 


70 


835io8 


41 


20 


161 164 


995390 


-3i 


165774 


14 


67 


834226 


40 


21 


9-162025 


14-33 


9-995372 


-31 


9-166654 


14 


64 


10-833346 


^I 


22 


162885 


i4-3o 


995353 


.31 


167532 


14 


61 


832468 


23 


163743 


14-27 


995334 


.31 


168409 


14 


58 


83i59i 


11 


24 


164600 


14-24 


995316 


.3i 


169284 


14 


55 


830716 


25 


165454 


14-22 


995297 


• 31 


170157 


14 


53 


829843 
828971 


35 


26 


i663o7 


14-19 
14-16 


995278 


-3i 


171029 


14 


5o 


34 


27 


167159 
168008 


995260 


-3i 


171899 


14 


47 


828101 


33 


28 


14-13 


995241 


•32 


172767 


14 


44 


827233 


32 


29 


168856 


14-10 


995222 


-32 


173634 


14 


42 


826366 


3i 


3o 


169702 


14-07 


995203 


-32 


174499 


14 


39 


825501 


3o 


3i 


9-170547 


i4-o5 


9-995184 


-32 


9-175362 


14 


36 


10-824638 


3 


32 


171389 


14-02 


995165 


•32 


176224 


14 


33 


823776 


33 


172230 


13-99 


995146 


-32 


177084 


14 


3i 


822916 


27 


34 


173070 


13-96 


995127 


•32 


177942 


14 


28 


822058 


26 


35 
36 


173908 
174744 


i3-94 
13-91 
13-88 


995108 
995089 


■32 
•32 


\fJM 


14 
14 


25 
23 


821201 
820345 


25 

24 


37 


175578 


995070 


•32 


i8o5o8 


U 


20 


IX% 


23 


38 


176411 


13-86 


995o5i 


•32 


i8i36o 


14 


17 


22 


39 


177242 


13-83 


c)95o32 


•32 


182211 


14 


i5 


817789 


21 


40 


178072 


i3-8o 


995oi3 


•32 


i83o59 


14 


12 


816941 


20 


41 


9-178900 


13-77 


9-994993 


•32 


9-183907 


14 


09 


10-816093 


;i 


42 


XI?, 


13-74 


994974 


-32 


184752 


14 


07 


8:5248 


43 


13-72 


994955 


-32 


185597 
186439 


14 


04 


8i44o3 


n 


44 


181374 


13-69 
13-66 


994935 


-32 


14 


02 


8i356i 


16 


45 


182196 


994916 
994896 


-33 


187280 


i3 


? 


812720 
811880 


i5 


46 


i83oi6 


13-64 


-33 


188120 


i3 


14 


47 


183834 


i3.6i 


994877 


-33 


188958 


i3 


,3 


811042 


i3 


48 


1 8465 1 


'.tU 


994857 


-33 


189794 


i3 




810206 


12 


49 


185466 


994838 


• 33 


190629 


i3 


89 


8of538 


II 


5o 


186280 


13-53 


994818 


• 33 


191462 


i3 


86 


10 


5i 


9.187092 


i3-5i 


9-994798 


■33 


9-192294 


i3 


^4 


10-807706 


I 


52 


187903 


i3-48 


994779 


•33 


193124 


i3 


81 


806876 


53 


188712 


13-46 


994759 


•33 


,93953 


i3 


79 


806047 


1 


54 


189519 
190325 


13-43 


994739 


• 33 


194780 


i3 


76 


8o522o 


6 


55 


13-41 


994719 


•33 


195606 


i3 


74 


804394 


5 


56 


i9ii3o 


13-38 


994700 


-33 


196430 


i3 


71 


803570 


4 


57 


19.933 


13-36 


994680 


-33 


XI 


i3 


69 


802747 


3 


58 


192734 


13-33 


994660 


-33 


i3 


66 


801926 


2 


59 


193534 


i3.3o 


994640 


• 33 


198894 


i3. 


64 


801106 


I 


60 


194332 


13.28 


994620 


•33 


199713 


i3 61 


800287 







Cosine 


D. 


Sine 


1 Cotans:- 


D. 


Tang. 


_i^-_ 



(81 DEGREES.) 



SINES AND TANGENTS. (9 DEGEEE.) 



27 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 







9.194332 


13-28 


9.994620 


-33 


9- 199713 


i3-6i 


10-800287 


60 


I 


195120 
195925 


13-26 


994600 


-33 


200529 
201345 


13-59 


]%ll 


59 


2 


i3-23 


994580 


-33 


13-56 


58 


3 


196719 


I3-2I 


994560 


•34 


202 1 5g 


13-54 


797841 


57 


4 


197D11 
198302 


i3-i8 


994540 


•34 


202971 


i3-52 


797020 
796218 


56 


5 


i3-i6 


994519 


•34 


203782 


13-49 


55 


6 


19909 1 


i3-i3 


994499 


•34 


204592 


.3-47 


795408 


54 


I 


199879 


I3-II 


994479 


•34 


205400 


13-45 


794600 


53 


200666 


i3-o8 


994459 
994438 


■34 


206207 


13-42 


793793 


52 


9 


20i45i 


i3-o6 


•34 


207013 


i3-4o 


792987 


5i 


10 


202234 


13-04 


994418 


•34 


207817 


13-38 


792183 


5o 


II 


9-2o3oi7 


I3-0I 


9.994397 


■34 


9-208619 


13-35 


10-791381 


8 


12 


203797 


12-99 


994377 


• 34 


209420 


13-33 


7^9780 
788982 


i3 


204577 


12-96 


994357 


•34 


210220 


i3-3i 


47 


U 


205354 


12-94 


994336 


•34 


211018 


13-28 


46 


i5 


2o6i3i 


12-92 

,2-§9 


994316 


•34 


2ii8i5 


13-26 


788185 


45 


i6 


206906 


994295 


•34 


212611 


13-24 


787389 
78659! 


44 


17 


207679 


12-87 


994274 


-35 


2i34o5 


I3-2I 


43 


18 


208452 


12-85 


994254 


-35 


214198 


13-19 


785802 


42 


19 


209222 


12-82 


994233 


-35 


214989 


13-17 


78501 1 


41 


20 


209992 


12.80 


994212 


-35 


215780 


i3-i5 


784220 


40 


21 


9.210760 

2Il526 


12-78 


9-994191 


• 35 


9-216568 


13-12 


10-783432 


3q 


22 


12-75 


9941 7 1 


-35 


217356 


i3-io 


782644 


38 


23 


2I229I 

2i3o55 


12-73 


9941 5o 


-35 


218142 


i3-o8 


781858 


u 


24 


12.71 


994129 


-35 


218926 


i3.o5 


781074 


25 


2i38i8 


12-68 


994108 


• 35 


219710 


i3-o3 


780290 


35 


26 


214579 
215338 


12-66 


994087 


-35 


220492 


13-01 


779508 


34 


27 


12-64 


994066 


-35 


221272 


12-99 


778728 


33 


28 


=:s?i 


12-61 


994045 


-35 


222052 


12-97 


777948 


32 


2g 


12.59 


994024 


-35 


222830 


12-94 


777170 


3i 


3o 


217609 


12.57 


994oo3 


•35 


2236o6 


12-92 


776394 


3o 


3i 


9-218363 


12-55 


9-993981 


-35 


9-224382 


12-90 
12-88 


10-775618 


11 


32 


219116 


12-53 


993960 


-35 


225i56 


774844 


33 


219868 


12. 5o 


liZ 


-35 


225929 


12-86 


774071 


27 


34 


220618 


12-48 


-35 


226700 


12-84 


773300 


26 


35 


22i367 


12-46 


-36 


227471 




772529 


25 


36 


2221l5 


12-44 


993875 


-36 


228239 


12-79 


771761 


24 


37 


222861 


12-42 


993854 


-36 


229007 


12-77 
12-75 


770993 


23 


38 


223606 


12.39 


993832 


-36 


229773 


770227 


22 


39 


224349 


12.37 


993811 


-36 


23o539 


12.73 


768698 


21 


40 


225092 


12.35 


993789 


• 36 


23l302 


12.71 


20 


41 


9.225833 


12-33 


9-993768 


•36 


9-232065 


12.69 


10-767935 


;? 


42 


226573 


12. 3i 


993746 


•36 


232826 


12.67 


767174 


43 


227311 


12.28 


993725 


• 36 


233586 


12.65 


766414 


\i 


44 


228048 


12.26 


993703 


•36 


234345 


12.62 


765655 


45 


228784 


12.24 


993681 


-36 


235io3 


12.60 


764897 


i5 


46 


229518 


12.22 


993660 


•36 


235859 


12.58 


764141 


i4 


8 


230252 


12.20 


993638 


• 36 


2366i4 


12.56 


763386 


i3 


230984 


12.18 


993616 


•36 


237368 


12-54 


762632 


12 


49 


23I7I4 


12-16 


993594 


•37 


238i2o 


12-52 


761880 


11 


5o 


232444 


12-14 


993572 


■37 


238872 


12-50 


761128 


10 


5i 


9-233172 


12-12 


9-993550 


• 37 


9-239622 


12-48 


10-760378 


I 


52 


233899 
234625 


12-09 


993528 


•37 


240371 


12-46 


%t 


53 


12-07 


993506 


■37 


241 118 


12-44 


1 


54 


235349 
236073 


12 -oS 


993484 


• 37 


24i865 


12-42 


758i35 


6 


55 


12.03 


993462 


•37 


242610 


12-40 


757390 


5 


56 


236795 


12-01 


993440 


.37 


243354 


12-38 


756646 


4 


57 
58 


2375i5 


XI. 99 


993418 


-37 


244097 
244839 


12-36 


755903 


3 


238235 


11.97 


993396 


•37 


12-34 


755161 


2 


59 


238953 


11.95 


993374 


•37 


245579 


12-32 


754421 


I 


60 


239670 


11-93 


993351 


• 37 


246319 


12-30 


753681 





i 


Cosine 


1 D. 


Sine 




Cotang. 


D. 


Tang. 


^ 



(80 DEGREES.) 



28 



(10 DEGREES.) A TABLE OF LOGARITHMIC 



'm. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 







9-239670 


11-93 


9.993351 


.37 


9-2463.9 


I2-3o 


10 -753681 


60 


I 


240386 


l\t 


993329 


-37 


247057 


12.28 


752943 


s 


2 


241101 


993307 


-37 


247794 


12-26 


752206 


3 


241814 


11-87 


993285 


-37 


248530 


12-24 


75.470 


57 


4 


242526 


11-85 


993262 


-37 


249264 


12-22 


7507.36 


56 


5 


243237 


11-83 


993240 


•37 


ISfo 


12-20 


750002 


55 


6 


243947 


11-81 


993217 


-38 


12-18 


749270 


54 


7 


244656 


11-79 


993195 


-38 


25.461 


\l.,l 


748539 


53 


8 


245363 


11-77 


993172 


■38 


25219. 


747809 


52 


9 


246069 


11-75 


993149 


• 38 


252920 


I2-I3 


747080 


5i 


10 


246773 


11-73 


993.27 


-38 


253648 


12-11 


746352 


5o 


II 


9-247478 


11-71 


9-993.04 


-38 


9-254374 


12^09 


10-745626 


S 


12 


24S181 


11-69 


99308. 


-38 


235.00 


12-07 


744900 


i3 


248883 


;::S 


993059 
993o36 


•38 


255824 


12-05 


744176 


47 


14 


249583 


-38 


256547 


i2-o3 


743453 


46 


i5 


2502S2 


11-63 


9930.3 


-38 


257269 


12-01 


742731 


45 


i6 


250980 
25.677 


I. -61 


992990 


■ 38 


2587.0 


12-00 


742010 


44 


17 


11-50 


992967 


-38 


11-98 


74.290 


43 


i8 


202373 


11-58 


992944 


-38 


259429 


11-96 


740571 


42 


19 


253067 


11-56 


992921 


•38 


260.46 


n-94 


739854 


41 


20 


253761 


11-54 


992898 


•38 


260863 


II^92 


739.37 


/,o 


21 


9-254453 


11-52 


9-992875 


•38 


9-26.578 


l\X 


10-738422 


It 


22 


255144 


I. -50 


992852 


•38 


262292 


737708 


23 


255834 


11-48 


sss 


-39 


263oo5 


11-8^ 


?af 


11 


24 


256523 


11-46 


-39 


2637.7 


ii^85 


25 


25721. 


11-44 


992783 


•39 


264428 


ii^83 


735572 


35 


26 


mis 


11-42 


992759 


•39 


265.38 


ii^8i 


734862 


34 


11 


11-41 


992736 


•39 


265847 


..■79 
..-78 


734153 


33 


259268 


11-39 


9927.3 


-39 


266555 


733445 


32 


29 


259951 


11-37 


992690 


.39 


26726. 


11-76 


f.iii 


3i 


3o 


260633 


11-35 


992666 


•39 


267967 


11-74 


3o 


3i 


9-26i3.4 


11-33 


9-992643 


• 39 


9-26867. 


11^72 


"t<iit 


3 


32 


261994 


ii-3i 


9926.9 


•39 


269375 


n^70 


33 


262673 


ii-3o 


992596 


•39 


270077 


1 1^69 


729923 


27 


34 


263351 


11-28 


992572 


-39 


270779 


11-67 


729221 
728521 


26 


35 


264027 


11-26 


& 


•39 


St?? 


11-65 


25 


36 


264703 


11-24 


-39 


11-64 


727822 


24 


37 


265377 


11-22 


99250. 


•39 


272876 


11-62 


727124 


23 


38 


26605 1 


11-20 


992478 
992454 


-40 


273573 


11-60 


726427 


22 


39 


266723 


11-19 


.40 


274269 


11-58 


72573. 


21 


40 


267395 


11-17 


992430 


• 40 


274964 


n-57 


725o36 


20 


41 


9-268065 


II-I5 


9-992406 


•40 


9-275658 


11.55 


10-724342 


19 


42 


268734 


11-13 


992382 


•40 


27635. 


11-53 


723649 


18 


43 


269402 


11-11 


& 


• 40 


277043 


ii-5i 


722957 


J7 


44 


270735 


11-10 


-40 


277734 


ii-5o 


722266 


16 


45 


11-08 


9923.. 


-40 


278424 


I .•48 


?2o887 


i5 


46 


27.400 


11-06 


992287 


-40 


279113 


I. -47 


14 


3 


272064 


ii-o5 


992263 


•40 


279801 


11-45 


720199 


i3 


272726 


ii-o3 


992239 


-40 


280488 


11-43 


]',& 


13 


49 


273388 


11-01 


992214 


•40 


281174 


11-4. 


II 


5o 


274049 


10-99 


992.90 


•40 


28.858 


11-40 


718142 


10 


5i 


9-274708 


10-98 


9-992166 


-40 


9-282542 


11-38 


10-717458 


t 


52 


273367 


10-96 


992.42 


-40 


283225 


11-36 


7.6775 


53 


276024 


10-94 


992. .7 


•4. 


283907 
284588 


11-35 


716093 


7 


54 


276681 


10-92 


992093 


•41 


1.-33 


7154.2 


6 


55 


277337 


lO-OI 


992069 


•41 


283268 


11-31 


714732 


5 


56 


278644 


10-89 


992044 


•41 


285947 


ii-3o 


714053 


4 


57 


10-87 


992020 


• 41 


286624 


11-28 


7.3376 


3 


58 


279297 


10-86 


99.996 


•41 


28730. 


1.^26 


712699 
712023 


2 


59 


IK 


10-84 


99.971 


•41 


'Iltll 


11^25 


I 


60 


10-82 


991947 


•41 


II^23 


71.348 







Cosine 


D. 


Sine 1 


Cotang. 


D. 


Tang. 1 M. | 



("79 DEGREES.) 



SINES AND TANGENTS. (11 DEGREES.) 



29 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Gotang. 


60 





9-280599 
281248 


10-82 


9-991947 


•41 


9-288652 


U-23 


10-711348 


I 


io-8i 


991922 


•41 


289326 


11-22 


710674 


It 


2 


28.897 


10-79 


991897 


•41 


289999 


11-20 


710001 


3 


282544 


10-77 


991873 


•41 


290671 


11-18 


709329 


57 


4 


283190 
283836 


10-76 


991848 


-41 


291342 


11-17 


708658 


56 


5 


10-74 


991823 


•41 


292013 


II..5 


To]f.l 


55 


6 


284480 


10-72 


991799 


•41 


292682 


ii-U 


54 


I 


285124 


10-71 


991774 


•42 


293350 


II-I2 


7o665o 


53 


285766 


10-69 


991749 


•42 


294017 


II^II 


705983 
7o53i6 


52 


9 


286408 


10-67 


991724 


-42 


294684 


11-09 


5i 


10 


287048 


10-66 


991699 


•42 


295349 


11-07 


704651 


5o 


II 


9.287687 


10-64 


9-991674 


•42 


9-296013 


II -06 


"■^SS 


S 


12 


288326 


10-63 


991649 


•42 


296677 


11-04 


i3 


288964 


io-6i 


991624 


-42 


297339 


1 1 -03 


702661 


47 


14 


289600 


lo^S 


991599 


•42 


298001 


II-OI 


?2;s 


46 


i5 


290236 


991574 


•42 


298662 


11-00 


45 


i6 


290870 


10-56 


991549 


■42 


299322 


10-98 


700678 


44 


11 


291504 


10-54 


991324 


-42 


2S 


10-96 


700020 


43 


292137 
292768 


10-53 


991498 


•42 


10-95 


698705 


42 


19 


io-5i 


991473 


•42 


801295 
3oi95i 


10-93 


41 


20 


293399 


io-5o 


991448 


•42 


10-92 


698049 


40 


21 


9-294029 


10-48 


9-991422 


•42 


9.302607 


10-90 


10-697393 


39 


22 


294658 


10-46 


991397 


•42 


3o326i 


10-89 


696739 


38 


23 


295286 


10-45 


991372 


•43 


303914 
304567 
3o52.8 


10-87 


696086 


37 


24 


295913 
296D39 


10-43 


991346 


•43 


10-86 


695433 


36 


25 


10-42 


991321 


•43 


10-84 


694782 


35 


26 


397164 


10-40 


991295 


•43 


3o5869 


10-83 


694131 


34 


27 


297788 


10-39 


991270 


•43 


3o65i9 
307168 


10-81 


693481 


33 


28 


298412 


10-37 

10-36 


991244 


•43 


io-8o 


692832 


32 


29 


299034 


991218 


•43 


307815 


10.78 


692185 


3i 


3o 


299655 


10-34 


991193 


•43 


3o8463 


10.77 


691537 


3o 


3i 


9-300276 


10-32 


9-991x67 


•43 


9-309109 


10-75 


10-690891 


29 


32 


300895 


io-3i 


991 i4i 


•43 


309754 


10-74 


690246 


28 


33 


3oi5i4 


10-29 
10-28 


991115 


•43 


310398 


10-73 


27 


34 


302l32 


991090 


•43 


311042 


10-71 


688958 


26 


35 


302748 


10-26 


991064 


•43 


3ii685 


10-70 
10-68 


68831 5 


25 


36 


3o3364 


10-25 


991038 


•43 


312327 


687673 


24 


ll 


3o3979 


10-23 


991012 


•43 


lltl 


10-67 


687033 


23 


304593 


10-22 


990986 


•43 


10-65 


686392 
685753 


22 


39 


3o5207 


10-20 


990960 


•43 


iniu 


10-64 


21 


40 


3o58i9 


10-19 


990934 


•44 


10-62 


685ii5 


20 


41 


9-3o643o 


10-17 


9-990908 
990882 


•44 


9-3i5523 


io-6i 


10-684477 


\l 


42 


307041 


10-16 


•44 


3i6i59 
316795 


10-60 


683841 


43 


3o765o 


10-14 


990855 


•44 


10-58 


683205 


\l 


44 


308259 


io-i3 


990829 
990803 


•44 


3 17430 
318064 


10-57 
10-55 


682570 


45 


308867 


lO-II 


•44 


681986 


i5 


46 


309474 


10-10 


990777 


•44 


318697 


10-54 


68i3o3 


14 


^l 


3ioo8o 


10-08 


990750 


•44 


319329 


10-53 


680671 


i3 


48 


3io685 


10-07 


990724 


•44 


319961 


I0-5I 


680039 
679408 


12 


49 


311289 


io-o5 


990697 


•44 


820092 


io-5o 


11 


5o 


311893 


10-04 


990671 


•44 


321222 


10-48 


678778 


10 


5i 


9-312495 


10 -o3 


9-990644 


•44 


9-32i85i 


10-47 


10.678149 


„ 


52 


3i3o97 


10-01 


990618 


•44 


322479 


10-45 


677521 


53 


313698 


10-00 


990591 


•44 


323io6 


10-44 


676894 


7 


54 


314297 


9-98 


990565 


•44 


323733 


10-43 


676267 


6 


55 


314897 


9-97 


990538 


•44 


324358 


10-41 


675642 


5 


56 


3 1 5495 


9-96 


9905 1 1 


•45 


324933 
325607 


10-40 


675017 


4 


P 


316092 
3i66§9 


9.94 


990435 


•45 


10-39 


674393 


3 


9-93 


990453 


•45 


326231 


10-87 


673769 


2 


59 


317284 


9-91 


990431 


•45 


326853 


10-36 


673147 


I 


60 


317879 


9.90 


990434 


•45 


327475 


10-35 


672525 







Cosine 


D. 


Sine 1 




Cotan?. 


D. 


Tang. 1 M. | 



(7S DEGREES.) 



30 



(12 DEGEEES.) A TABLE OF LOGAEITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 




i ° 


9.317879 
318473 


9.90 


9-990404 


•45 


'tiS,i 


10.35 


10-672526 


60 


I 


9 


88 


&1 


-45 


10.33 


671905 




2 


319066 


9 


87 


-45 


328715 


10.32 


671285 


3 


319658 


9 


86 


990324 


•45 


329334 


10. 3o 


670666 


1 


4 


320249 


9 


84 


990297 


-45 


329953 

33o57o 


10.29 


670047 


5 


320840 


9 


83 


990270 


•45 


10.28 


669430 
6688i3 


55 


6 


321430 


9 


82 


990243 


-45 


331187 


10.26 


54 


7 


322019 


9 


80 


990215 


•45 


33i8o3 


10-25 


668,97 
667582 


53 


8 


322607 


9 


79 


990188 


•45 


332418 


10.24 


52 


9 


323194 
323780 


9 


]l 


990161 


•45 


333o33 


10.23 


666967 


5i 


10 


9 


990134 


•45 


333646 


10.21 


666354 


5o 


n 


9-324366 


9 


75 


9-990107 


.46 


9.334259 


10.20 


10.66574, 


3 


12 


324950 
325534 


9 


73 


990079 


-46 


334871 
335482 


10.19 


665,29 


i3 


9 


72 


990o52 


•46 


10.17 


6645,8 


47 


14 


326117 


9 


70 


990025 
989997 


.46 


336093 


10.16 


663907 
663298 
662689 


46 


i5 


326700 


9 


ll 


-46 


336702 
337311 


10.15 


45 


i6 


327281 


9 


989070 


-46 


10-13 


44 


\l 


327862 


9 


66 


989942 


•46 


Ss;? 


10-12 


66208, 


43 


328442 


9 


65 


989915 


•46 


10-11 


66,473 


42 


19 


329021 


9 


64 


989887 


-46 


339133 


10-10 


660867 


41 


20 


329599 


9 


62 


989860 


•46 


339739 


10-08 


660261 


40 


21 


9-330176 


9 


61 


9-989832 


•46 


9-340344 


10-07 


10.659656 


3^ 


22 


330753 


9 


60 


989804 


.46 


itif. 


10-06 


659052 
658448 


23 


33i329 


9 


58 


989777 


.46 


10.04 


37 


24 


331903 


9 


u 


989749 


•47 


342155 


10. o3 


657845 


36 


25 


332478 
333o5i 


9 


989721 


•47 


342757 


10.02 


657243 


35 


26 


9 


54 


989693 


•47 


343358 


10.00 


656642 


34 


S 


333624 


9 


53 


989665 


•47 


343958 
344558 


9.99 
9.98 


656042 


33 


334195 


9 


52 


989637 


•47 


655442 


32 


29 


334766 


9 


5o 


989609 


•47 


345i57 


9-97 


654843 


3i 


3o 


335337 


9 


49 


989582 


•47 


345755 


9.96 


654245 


3o 


3i 


9-335906 


9 


48 


9.989553 


•47 


9-346353 


9.94 


10-653647 


S 


32 


336475 


9 


46 


989525 


-47 


im 


9-93 


653o5i 


33 


337043 


9 


45 


989497 


■47 


9-92 


652455 


27 


34 


337610 


9 


44 


989469 


•47 


348141 


9.91 


65 1859 
65,265 


26 


35 


338176 


9 


43 


989441 


•47 


348735 


9.90 


25 


36 


338742 
339306 


9 


41 


9894.3 


•47 


349329 


9.88 


650671 


24 


ll 


9 


40 


989384 


•47 


349922 
35o5i4 


It 


650078 


23 


339871 


9 


39 


989356 


•47 


649486 
648894 


22 


39 


340434 


9 


37 


989328 


•47 


35iio6 


9.85 


21 


40 


340996 


9 


36 


989300 


•47 


35,697 


9.83 


6483o3 


20 


41 


9-341558 


9 


35 


9-989271 


•47 


9-352287 


9.82 


10-647713 


;? 


42 


342119 


9 


34 


989243 


•47 


352876 


9.81 


647124 


43 


342679 


9 


32 


989214 


•47 


353465 


9-80 


646535 


n 


44 


343239 


9 


3i 


989186 


-47 


354053 


9-79 


645947 
645360 


16 


45 


ISs? 


9 


3o 


989,57 


•47 


354640 


t^l 


i5 


46 


9 


29 


989128 


.48 


355227 
3558,3 


644773 


14 


47 


344912 


9 


27 


989100 


.48 


9.75 


644187 


i3 


48 


345469 


9 


26 


989071 


■ 48 


3563o8 


9-74 


643602 


12 


49 


346024 


9 


25 


989042 


-48 , 


35^^66 


9.73 


643018 


II 


5o 


346579 


9 


24 


989014 


• 48 


9.71 


642434 


10 


5i 


9-347134 


9 


22 


9.988985 


.48 


9-358,49 


9.68 


io.64i85i 


9 


52 


347687 


9 


21 


988956 


•48 


358731 


641269 


8 


53 


348240 


9 


20 


ftj 


.48 


359313 


640687 


7 


54 


348792 


9 


19 


• 48 


359893 


9.67 


640107 


6 


55 


349343 


9 


17 


988869 


.48 


360474 
36io53 


9.66 


639526 
638947 
638368 


5 


56 


349893 


9 


16 


988840 


.48 


9.65 


4 


57 


350443 


9 


i5 


988811 


•49 


36i632 


9.63 


3 


58 


li:ni 


9 


14 


988782 


-49 


362210 


9.62 


637790 


2 


59 


9 


i3 


988753 


•49 


362787 


9.61 


6372,3 


I 


60 


352088 


9. II 


988724 


.49 


363364 


9.60 


636636 







Cosine 


D. 


Sine 


Cotan^. 


D. 


Tang. M. | 



(77 DEGREES.) 



SINES AND TANGENTS. (13 DEGEEES.) 



31 



M. 




Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 




g. 352088 


9. II 


9.988724 


.49 


9-363364 


9-60 


10-636636 


60 


I 


352635 


9 


10 


988695 


.49 


363940 


9 


59 


636o6o 


u 


2 


353i8i 


9 


S 


988666 


•49 


364315 


9 


58 


635485 


3 


353726 


9 


988636 


■49 


365090 
365664 


9 


57 


634910 
634336 


57 


4 


354271 


9 


07 


988607 
988578 


•49 


9 


55 


56 


5 


354815 


9 


o5 


•49 


366237 


9 


54 


633763 


55 


6 


355358 


9 


04 


988548 


.49 


366810 


9 


53 


633190 


54 


I 


355901 


9 


o3 


q885i9 


•49 


367382 


9 


52 


632618 


53 


356443 


9 


02 


988489 


•49 


367953 
368524 


9 


5i 


632047 


52 


9 


356984 
357624 


t 


01 


988460 


.40 


9 


5o 


631476 


5i 


10 


99 


988430 


•49 


369094 


9 


49 


630906 


5o 


II 


9 -358064 


8 


98 


9.988401 


•49 


9.369663 


9 


48 


io-63o337 


8 


12 


3586o3 


8 


97 


•988371 


•49 


370232 


9 


46 


629768 


i3 


359141 


8 


96 


988342 


.49 


370799 


9 


45 


629201 


47 


14 


359678 


8 


95 


9883x2 


.5o 


371367 


9 


44 


623633 


46 


i5 


36o2i5 


8 


93 


988282 


.5o 


371933 


9 


43 


628067 


45 


i6 


360752 


8 


92 


988252 


.5o 


372499 


9 


42 


627501 


44 


\l 


361287 


8 


91 


988223 


.5o 


373064 


9 


41 


626936 
626371 


43 


361822 


8 




988193 


•5o 


373629 


9 


40 


42 


19 


362356 


8 


sl 


988163 


.5o 


374193 
374756 


9 


ll 


625807 


41 


20 


362889 


8 


988133 


.50 


9 


623244 


40 


21 


0.363422 


8 


87 


9.988103 


.50 


9.375319 


9 


37 


10-624681 


39 
38 


22 


363954 


8 


85 


988073 


.50 


375881 


9 


35 


624119 
623558 


23 


364485 


8 


84 


988043 


.5o 


376442 


9 


34 


37 


24 


365oi6 


8 


83 


988013 


.5o 


377003 


9 


33 


622997 
622437 


36 


25 


355546 


8 


82 


987983 


• 5o 


377563 


9 


32 


35 


26 


366075 


8 


81 


987953 


.5o 


378122 


9 


3i 


621878 


34 


11 


366604 


8 


80 


987922 
987892 


.5o 


378681 


9 


3o 


621319 


33 


367i3i 


8 


79 


.50 


379239 


9 


ll 


620761 


32 


29 


367659 


8 


77 


987862 


.5o 


lai 


9 


620203 


3i 


3o 


368i85 


8 


76 


987832 


.5i 


9 


27 


619646 


3o 


3i 


9.368711 


8 


75 


9.987801 




9-380910 


9 


26 


10-619090 
618534 


29 


32 


369236 


8 


74 


987771 




381466 


9 


25 


28 


33 


369761 


8 


73 


987740 




382020 


9 


24 


617980 


2 


34 


370285 


8 


72 


987710 




382575 


9 


23 


617425 


35 


370808 


8 


71 


987679 




383129 


9 


22 


616871 


25 


36 


37i33o 


8 


70 


987649 




383682 


9 


21 


6i63i8 


24 


ll 


371852 


8 


69 


987618 




384234 


9 


20 


615766 


23 


372373 


8 


tl 


987588 




384786 


9 


\l 


6i52i4 


22 


39 


372894 


8 


987557 




385337 


9 


614663 


21 


40 


373414 


8 


65 


987526 




385888 


9 


17 


614112 


20 


41 


9.373933 


8 


64 


9-987496 
987463 




9-386438 


9 


i5 


io.6i3562 


\l 


42 


374452 


8 


63 




386987 
387536 


9 


14 


6i3oi3 


43 


374970 


8 


62 


987434 




9 


i3 


612464 


17 


H 


375487 


8 


61 


987403 


.52 


388o84 


9 


12 


611916 


16 


45 


376003 


8 


60 


687372 


.52 


388631 


9 


II 


611369 


i5 


46 


376519 
377035 


8 


1 


987341 


•52 


389178 


9 


10 


610822 


14 


47 


8 


987310 


•52 


389724 


9 


0^ 


610276 


i3 


48 


377549 
378063 


8 


57 


987270 
987248 


.52 


390270 


9 


609730 


12 


^9 


8 


56 


.52 


390815 


9 


07 


609185 
608640 


II 


5o 


378577 


8 


54 


987217 


.52 


391360 


9 


06 


10 


5i 


9.379089 


8 


53 


9.987186 


.52 


9-391903 


9 


o5 


10-608097 


I 


02 


379601 


8 


52 


987155 


■52 


392447 


9 


04 


607533 


53 


38oii3 


8 


5i 


987124 


.52 


392989 


9 


o3 


60701 1 


1 


54 


380624 


8 


5o 


987092 


.52 


39333 1 


9 


02 


. 606469 


6 


55 


38ii34 


8 


S 


987061 


.52 


394073 


9 


01 


603927 
6o5386 


5 


56 


381643 


8 


987030 


.52 


394614 


I 


00 


4 


s 


382152 


8 


47 


986998 


.52 


393.54 


9^ 


604846 


3 


382661 


8 


46 


986967 


.52 


395694 
396233 


8 


604306 


2 


59 


383 1 68 


8 


45 


986936 


.52 


8 


Q7 


603767 


I 


60 


383675 


8.44 


986904 


.52 


396771 


8-96 


603229 







Cosine 


D. 


Sine 




Cotang. 


D. 


Tan?. 


mT 



(76 DEGREES.) 



82 



(14 DEGREES.) A TABLE OF LOGAEITHMIC 



M. 




Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 




0-383675 


8.44 


'ttl'i 


•52 


9.396771 


8.96 


10.603229 


60 


I 


384182 


8 


43 


■ 53 


397309 


8 


96 


602691 
602 1 54 


59 


2 


384687 


8 


42 


986841 


.53 


397846 


8 


.95 


58 


3 


385192 


8 


41 


986809 


.53 


398383 


8 


94 


601617 


57 


4 


385697 


8 


40 


986778 


•53 


'& 


8 


93 


601081 


56 


5 


386201 


8 


ll 


986746 


.53 


8 


92 


600545 


55 


6 


386704 


8 


9867.4 


.53 


399990 


8 


91 


600010 


54 


7 


387207 


8 


37 


986683 


.53 


4oo524 


8 




II 


53 


8 


387709 


8 


36 


986651 


.53 


4oio58 


8 


52 


9 


388210 


8 


35 


986619 


•53 


401591 


8 


597876 


5i 


10 


388711 


8 


34 


986587 


.53 


402124 


8 


87 


5o 


II 


9.389211 


8 


33 


9.986555 


.53 


9.402656 


8 


86 


10.597344 


8 


12 


38971 1 


8 


32 


986523 


.53 


403187 


8 


85 


596813 


i3 


390210 


8 


3i 


986491 


• 53 


403718 


8 


84 


5962S2 


47 


14 


390708 


8 


3o 


986459 


• 53 


404249 
404778 


8 


83 


595751 


46 


ID 


391206 


8 


28 


986427 


.53 


8 


82 


595222 


45 


i6 


391703 


8 


U 


9S6395 


■53 


4o53o8 


8 


8i 


594692 


44 


n 


392199 


8 


986363 


•54 


405836 


8 


80 


594164 


43 


i8 


392695 


8 


25 


986331 


•54 


406364 


8 


?§ 


593636 


42 


19 


393191 


8 


24 


$11^ 


•54 


406892 


8 


593108 


41 


20 


393685 


8 


23 


•54 


407419 


8 


77 


592581 


40 


21 


9.394179 
394673 


8 


22 


9.986234 


•^4 


9.407945 


8 


■7^ 


10.592055 


39 


22 


8 


21 


986202 


•54 


408471 


8 


75 


59.529 


38 


23 


395166 


8 


20 


986169 


•54 


408997 
409521 


8 


74 


59.003 


u 


24 


395658 


8 


1? 


986137 


•54 


8 


74 


t& 


2D 


396150 


8 


986104 


•54 


410045 


8 


73 


35 


26 


396641 


8 


17 


986072 


•54 


410569 


8 


72 


58043 1 
588908 


34 


11 


397132 


8 


ll 


986039 


•54 


411092 


8 


71 


33 


itr. 


8 


986007 


•54 


4ii6i5 


8 


70 


588385 


32 


29 


8 


i5 


985974 


•54 


412137 


8 


ll 


587863 


3i 


3o 


398600 


8 


14 


985942 


•54 


412658 


8 


587342 


3o 


3i 


9.399088 


8 


i3 


'■llU7 


■ 55 


9-4i3i79 


8 


67 


10.586821 


3 


32 


399575 


8 


12 


.55 


413699 


8 


66 


586301 


33 


400062 


8 


II 


985843 


• 55 


414219 
414738 


8 


65 


585781 


27 
26 


34 


400549 


8 


10 


98581 1 


• 55 


8 


64 


585262S 


35 


4oio35 


8 


o§ 


985778 


• 55 


415257 


8 


64 


584743 


25 


36 


4oi52o 


8 


985745 


• 55 


415775 


8 


63 


5842 25 


24 


11 


4o2oo5 


8 


07 


985712 


.55 


416293 


8 


62 


583707 


23 


402489 


8 


06 


985679 


.55 


416810 


8 


61 


583.90 


22 


39 


402972 


8 


o5 


985646 


■ 55 


417326 


8 


60 


582674 


21 


40 


403455 


8 


04 


9856 1 3 


■ 55 


417842 


8 


59 


582158 


20 


41 


9.403938 


8 


o3 


9.985580 


■ 55 


9.418358 


8 


58 


.0.58.642 


It 


42 


404420 


8 


02 


985547 


■ 55 


418873 


8 


57 


58.127 


43 


404901 


8 


01 


985514 


■ 55 


419387 


8 


56 


5806.3 


17 


44 


405382 


8 


00 


985480 


■ 55 


419901 


8 


55 


?» 


.6 


45 


4o5862 


7 


?? 


985447 


■ 55 


420415 


8 


55 


i5 


46 


406341 


7 


985414 


■ 56 


420927 


8 


54 


nr£ 


i4 


a 


406820 


7 


97 


985380 


• 56 


421440 


8 


53 


i3 


407299 


7 


96 


985347 


■ 56 


421952 


8 


52 


578048 


12 


49 


407777 


7 


95 


985314 


• 56 


42 2463 


8 


5i 


577537 


II 


5o 


408254 


7 


94 


985280 


• 56 


422974 


8 


5o 


577026 


10 


5i 


9.408731 


7 


94 


9-985247 


■ 56 


9.423484 


8 


4q 
48 


.0.5765.6 


I 


52 


409207 


7 


93 


985213 


■56 


423993 


8 


576007 


53 


409682 


7 


92 


985180 


■ 56 


4245o3 


8 


48 


lix 


7 


54 


410157 


7 


91 


985146 


• 56 


425ou 


8 


47 
46 


6 


55 


410632 


7 




985ii3 


• 56 


425519 


8 


574481 


5 


56 


411106 


7 


1 


985079 
985045 


• 56 


426027 


8 


45 


573973 


4 


S 


41 1 579 
4i2o52 


7 


• 56 


426534 


8 


44 


573466 


3 


7 


87 


98501 1 


• 56 


427041 


8 


43 


572959 


2 


59 


412524 


7 


86 


984978 


• 56 


427547 


8 


43 


572453 


I 


60 


412996 


7 85 


984944 


• 56 


428052 


8 42 


57.948 







Cosine 


D. 


Sine 




Cotang. 


D. 


Tang. 


"m7 



(75 DEGREES. 



SINES AND TANGENTS. (15 DEGREES.) 



83 



M. 


Siae 


D. 


Cosine ■ 


D. 


Tang. 


D. 


Cotang. 







'■lis? 


7-85 


9.984944 


•^ 


9 •428052 


8.42 


10-571948 


60 


I 


7-84 


984910 


•57 


428557 


8 


41 


57.443 


1? 


2 


413938 


7-83 


984876 


■P 


429062 


8 


40 


570938 


3 


414408 


7-83 


984842 


•57 


429566 


8 


U 


570434 


u 


4 


414878 


7-82 


984808 


•57 


430070 


8 


569930 


5 


415347 


7-8i 


934774 


•57 


430573 


8 


38 


X'l 


55 


6 


4i58i5 


7-80 


984740 


•57 


431075 


8 


37 


54 


7 


416283 


7-79 


984706 


•57 


43.577 


8 


36 


568423 


53 


8 


416751 


7-78 


9S4672 


•57 


432079 


8 


35 


06792. 


52 


9 


417217 


7-77 


984637 


17 


432580 


8 


34 


567420 


5i 


10 


4.7684 


7-76 


984603 


•57 


433080 


8 


33 


566920 


5o 


II 


9-4i8i5o 


7-75 


9.984569 


■57 


9^433580 


8 


32 


10-566420 


it 


12 


4i86i5 


7-74 


\ 984535 


•57 


434080 


8 


32 


565920 


i3 


419079 


7-73 


984500 


•57 


435o]^ 


8 


3i 


56542. 


2 


14 


■419544 


7-73 


984466 


•^2 


8 


3o 


564922 


ID 


420007 


7-72 


984432 


• 58 


435576 


8 


29 


564424 


45 


i6 


420470 


7-71 


984397 


-58 


436073 


8 


28 


563927 


44 


•7 


420933 


7-70 


984363 


• 58 


436570 


8 


28 


563430 


43 


i8 


421395 
421857 
4223i8 


m 


984328 


-58 


437067 


8 


S 


562933 


42 


•9 


ii$n 


• 58 


437563 


8 


562437 


41 


20 


7-67 


• 58 


438o59 


8 


25 


561941 


40 


21 


9.422778 


7.67 


9.984224 


• 58 


9-438554 


8 


24 


10.561446 


ll 


22 


423238 


7-66 


?g;?i 


• 58 


439048 


8 


23 


560952 


23 


423697 


7-65 


• 58 


439543 


8 


23 


560457 


37 


24 


4241 56 


7-64 


984120 


• 58 


44oo36 


8 


22 


559964 


36 


23 


4246 1 5 


7-63 


984085 


• 58 


44o529 


8 


21 


559471 


35 


26 


425073 


7-62 


984050 


• 58 


441022 


8 


20 


558978 
558486 


34 


27 


425530 


7-6i 


984015 


• 58 


44i5i4 


8 


19 


33 


28 


425987 


7-6o 


983981 


• 58 


442006 


8 




557994 


32 


29 


426443 


7-60 


983946 


• 58 


442988 


8 


18 


5575o3 


3i 


3o 


426899 


7-59 


983911 


• 58 


8 


17 


557012 


30 


3i 


9-427354 


7-58 


9-983875 


• 58 


9-443479 


8 


16 


10-556521 


ll 


32 


427809 


7-57 


983840 


19 


443968 


8 


16 


556o32 


33 


428263 


7-56 


983805 


• 59 


444458 


8 


i5 


555542 


27 


34 


428717 


7-55 


983770 


• 59 


IISS 


8 


14 


555o53 


26 


35 


429170 


7-54 


983735 


.59 


8 


i3 


554565 


25 


36 


429623 


7-53 


983700 


19 


445923 


8 


12 


554077 


24 


ll 


430075 


7-52 


983664 


• 59 


44641 1 


8 


12 


553589 


23 


43o527 
430978 


7-52 


983629 


• 59 


446898 


8 


n 


553102 


22 


39 


7-5i 


983594 


• 59 


447384 


8 


10 


552616 


21 


40 


431429 


7-5o 


983558 


.59 


447870 


8 


09 


552130 


20 


4i 


9-431879 


7-49 


9-983523 


.59 


9-448356 


8 


09 


io-55i644 


;? 


42 


432329 
432778 


111 


933487 


•59 


448841 


8 


08 


55ii59 


43 


983452 


• 59 


449326 


8 


07 


550674 


17 


44 


433226 


7-47 


983416 


• 59 


449810 


8 


06 


550190 


16 


45 


433675 


7-46 


983381 


.59 


450294 


8 


06 


549706 


i5 


46 


434122 


7-45 


98334D 


.59 


430777 


8 


o5 


549223 
548740 


14 


^l 


434569 


7-44 


983309 ! 


•59 


45.260 


8 


04 


i3 


48 


435oi6 


7-44 


983273 i 


• 60 


45.743 


8 


o3 


548257 


12 


P 


435462 


7-43 


983238 ' 


• 60 


452225 


8 


02 


547775 


II 


5o 


435908 


7-42 


983202 


• 60 


452706 


8 


02 


547294 


10 


5i 


9-436353 


7-41 


9.983166 


• 60 


'tl&l 


8 


01 


io.5468i3 


9 


52 


436798 


7-40 


983 i3o 


■ 60 


8 


00 


546332 


8 


53 


437242 


7-40 


983094 


■ 60 


454148 




99 


545852 


I 


54 


437686 


7-39 


983o58 


.60 


454628 




?? 


545372 


55 


438129 


7-38 


983022 


• 60 


455.07 
455586 




544893 


5 


56 


438572 


7-37 


982986 


• 60 




97 


544414 


4 


^2 


439014 


7-36 


982950 


• 60 


456064 




96 


543936 


3 


53 


439456 


7-36 


982914 
982878 


• 60 


456542 




96 


543458 


2 


^ 


as? 


7-35 


• 60 


457019 
457496 




q5 


542981 
542504 


I 


6o 


7-34 


982842 


• 60 


7-94 







Cosine 


D. 


Sine 1 




Cotang. 


D. 


Tans. 


M. 



(74 DKGREES.) 



i 

! 














i : 


34 


(16 


DEGREES.) A TABLE OF LOGARITHMIC 






M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D- 


Cotang. 









9-440338 


7-34 


9-982842 


60 


9-457496 


7-94 


10-542504 


60 




I 


440778 




33 


982805 


60 


457973 


7-93 


542027 


58 






2 


441 2 18 




32 


982769 


61 


458440 
458925 


7-93 


54i55i 






3 


441658 




3i 


982733 


61 


7-92 


541075 


57 






4 


442096 




3i 


982696 


61 


459400 


7-91 


540600 


56 






5 


442535 




3o 


982660 


61 


459875 


7-90 


540125 


55 






6 


442973 




29 


982624 


61 


460349 


7-po 


539651 


54 






I 


443410 




28 


982587 


61 


460823 


539177 


53 




i 


443847 




27 


982551 


61 


461297 


538703 


52 






9 


444284 




27 


982514 


61 


461770 


7-88 


538230 


5i 






10 


444720 




26 


982477 


61 


462242 


7-87 


537758 


5o 






II 


9-445i55 




25 


9-982441 


61 


9-462714 


7-^^ 


10-537286 


49 






12 


445590 




24 


982404 


6i 


463 1 86 


7-85 


536814 


48 






i3 


446025 




23 


982367 


61 


463658 


7-85 


536342 


47 






14 


446459 




23 


982331 


61 


464129 


7-84 


535871 


46 






i5 


446893 




22 


982294 
982257 


61 


464599 


71^ 


535401 


45 






i6 


447326 




21 


61 


465069 


7-83 


534931 


44 






\l 


447759 




20 


982220 


62 


465539 
466008 


7-82 


534461 


43 






448191 




20 


982183 


62 


7-81 


533992 
533624 


42 






19 


448623 




11 


982146 


62 


466476 


7-8o 


41 






20 


449054 




982109 


62 


466945 


7-8o 


533o55 


40 




I 


21 


9-449485 




17 


9-982072 


62 


9-467413 


'r^s 


10-532587 


3q 






22 


449915 




16 


982035 


62 


467880 


532120 


38 






23 


45o345 




16 


981998 


62 


468347 


7-78 


53 1 653 


37 




1 


24 


450775 




i5 


981961 


62 


468814 


7-77 


53 1 186 


36 






25 


45 1204 




14 


981924 


62 


469280 


7-76 


530720 


35 






26 


45i632 




i3 


981886 


62 


469746 


7-75 


530254 


34 






27 


452060 




i3 


981849 


62 


4702 1 1 


7-75 


529789 


33 






28 


452488 




12 


9S1812 


62 


470676 


7-74 


529324 
52S859 


32 






29 


452gl5 




1 1 


981774 


62 


471141 


7-73 


3i 




1 


3o 


453342 




10 


981737 


62 


471605 


7-73 


528393 


3o 




1 ' 


3i 


9-453768 




10 


9-981699 


63 


9-472068 


7-72 


10-527932 


3 




1 


32 


454194 




09 


981662 


63 


472532 


7-71 


527468 




1 


33 


454619 




08 


981625 


63 


472995 


7-71 


527005 


27 




1 


34 


455044 




07 


98.587 


63 


473457 


7-70 


526543 


26 




1 


35 


455469 




07 


981549 


63 


473919 


7.69 


526081 


25 






36 


455893 




06 


981512 


63 


474381 


7-69 


52561Q 


24 






37 


4563i6 




o5 


9S1474 


63 


474842 


7-6§ 


525 1 58 


23 






38 


456739 




04 


981436 


63 


4753o3 


7-67 


524697 
524237 


22 






39 


457162 




o4 


981399 


63 


475763 


7-67 


21 






40 


457584 




o3 


981361 


63 


476223 


7-66 


523777 


20 






41 


9 -458006 


I 


02 


9-981323 


63 


9-476683 


7-65 


10-523317 


11 






42 


458427 




01 


981285 


63 


477142 


7-65 


522858 






43 


458848 


7 


01 


981247 


63 


Ti 


7-64 


522399 


17 






44 


459268 




00 


981209 


63 


7-63 


521941 


16 






45 


459688 


6 


n 


981171 


63 


478517 


7-63 


521483 


i5 






46 


460108 


6 


981133 


64 


478975 


7.62 


521025 


14 






8 


460527 


6 


98 


981095 


64 


479432 


7-61 


520568 


i3 






460046 


6 


97 


981037 


64 


f& 


7-61 


5201II 


12 






49 


461364 


6 


96 


981019 


64 


7-6o 


519655 


II 






5o 


461782 


6 


95 


980981 


64 


480801 


7-59 


519199 


ID 






5i 


9-462199 


6 


95 


9-980942 


64 


9-481257 


71§ 


10-518743 


t 






52 


462616 


6 


94 


980904 
980866 


64 


481712 


7-5§ 


518288 






53 


463o32 


6 


93 


64 


482167 


7-57 


517833 


1 






54 


463448 


6 


93 


980827 


64 


482621 


7-57 


517379 
516925 


6 






55 


463864 


6 


92 


980789 


64 


483075 


7-56 


5 






56 


464279 


6 


91 


980750 


64 


483529 


7-55 


516471 


4 






57 


464694 


6 


90 


980712 


64 


483982 


7-55 


5i6oi8 


3 






58 


465 1 08 


6 


90 


980673 


64 


484435 


7-54 


5i5565 


2 






59 


465522 


6 


89 


980635 


64 


484887 


7-53 


5i5ii3 


I 






60 


465935 


6-88 


980596 


64 


485339 


7-53 


5i466i 









Cosine 


D. 


Sine 


Cotang. 


D. 


Tang. 


11 












(V3d 


EGR 


EES.) 











SINES AND TANGENTS. (17 DEGEEES.) 



85 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotimg. 







9-465935 
466348 


6-88 
6-88 


980558 


64 
64 


9-485339 
485791 




55 

52 


IO-5I466! 
514209 


60 


2 


466761 


6-87 


980519 


65 


486242 




5i 


5.3758 


3 


467173 


6-86 


980480 


65 


486693 




5i 


5 1 3307 


57 


4 


467585 


6-85 


980442 


65 


487143 




5o 


512837 


56 


5 


467996 


6-85 


980403 


65 


487593 




49 


512407 


55 


6 


468407 


6-84 


980364 


65 


488043 




49 


51.957 


54 


7 


468817 


6-83 


980325 


65 


488492 




48 


5ii5o8 


53 


8 


469227 


6-83 


980286 


65 


488941 




47 


5iio59 


52 


9 


469637 


6-82 


980208 


65 


489390 




47 


5io6io 


5i 


10 


470046 


6-8i 


65 


489838 




46 


510162 


5o 


II 


9-470455 


6-8o 


9-980169 


65 


9-490286 




46 


10-509714 


ii 


12 


470863 


6-80 


980130 


65 


490733 




45 


50^820 


i3 


471271 


V^ 


980052 


65 


491 180 




44 


47 


U 


sa 


65 


491627 




44 


5o8373 


46 


i5 


6-78 


980012 


65 


492073 




43 


507927 


45 


i6 


472492 


6-77 


979973 


65 


492965 




43 


507481 


44 


\l 


472898 


6-76 


979833 


66 




42 


5o7o35 


43 


473304 


6-76 


66 


493410 




41 


5o6590 


42 


19 


473710 


6-75 


66 


493854 




40 


5o6i46 


41 


20 


4741 1 5 


6-74 


979816 


66 


494299 




40 


505701 


40 


21 


9-474519 
474923 


6-74 


9-979776 


66 


9-494743 




40 


io-5o5257' 


39 


22 


6.73 


979737 


66 


495186 




It 


5o48i4 


38 


23 


475327 


6-72 


l]& 


66 


493630 




504370 


37 


24 


475730 


6-72 


66 


496073 




37 


503927 


36 


25 


476133 


6-71 


979618 


66 


4965 1 5 




37 


5o3485 


35 


26 


476536 


6-70 


979579 


66 


496957 




36 


5o3o43 


34 


11 


476938 
477340 


6-69 


979539 


66 


497399 




36 


5o26oi 


33 


6-69 
6-68 


979499 


66 


497841 




35 


5o2i39 


32 


29 


477741 
478142 


979459 


66 


498282 




34 


501718 


3i 


3o 


6-67 


979420 


66 


498722 




34 


501278 


3o 


3i 


9-478542 


6-67 


9-979380 


66 


9-499163 




33 


io-5oo837 


li 


32 


478942 


6.66 


979340 


66 


499603 




33 


499958 
499519 


33 


479342 


6-65 


979300 


67 


5ooo42 




32 


27 


34 


479741 


6-65 


97,9260 


67 


5oo48i 




3i 


26 


35 


480140 


6-64 


979220 


67 


500920 
5oi359 




31 


« 


25 


36 


480539 


6-63 


979180 


67 




30 


24 


37 


480937 


6-63 


979140 


67 


tim 




30 


498203 


23 


38 


481334 


6-62 


979100 


67 




11 


497765 


22 


39 


481731 


6.61 


979039 


67 


502672 




497328 


21 


40 


482128 


6.61 


979019 


67 


5o3i09 




28 


496891 


20 


41 


9.482525 


6-60 


9-978979 


67 


9-5o3346 


7 




10-496454 


;? 


42 


482921 


6-59 


vM 


67 


503982 


7 




496018 


43 


4833 1 6 


6.59 
6-58 


67 


5o44i8 


7 




495582 


\i 


44 


483712 


67 


504854 






495146 


45 


484107 


6-57 


978817 


67 


505289 






4947 1 1 


i5 


46 


484501 


6-57 


978777 


67 


5o5724 






494276 


14 


S 


484895 
485289 


6-56 


978736 


67 


5o6i59 






493841 


i3 


6-55 


978696 


68 


506593 






493407 


12 


P 


485682 


6.55 


978635 


68 


507027 






492973 


II 


5o 


486075 


6-54 


978615 


68 


507460 






492340 


10 


5i 


9-486467 


6-53 


9-978574 


68 


9-507893 






10-492107 


g 


52 


486B60 


6-53 


978533 


68 


5o8326 






491674 


8 


53 


487251 


6-52 


978493 


68 


508759 




20 


491 241 


7 


54 


487643 


6.5i 


978452 


68 


509191 




19 


490800 
400378 
489946 
489515 


6 


55 


488034 


6.5i 


978411 


68 


509622 




19 


5 


56 


488424 


6-5o 


978370 


68 


5ioo54 




18 


4 


57 


488814 


6-5o 


978329 
978288 


68 


5 10485 




18 


3 


58 


489204 


6-48 


68 


510916 




17 


489084 
488654 


2 


59 


489593 


978247 


68 


5ii346 




16 


I 


60 


489982 


6-48 


978206 


68 


511776 


5-i6 


488224 





1 Cosine 


D. 


Sine 


D. 


Cotancr. 


D. 


Tang. 


~m7 



17 



(72 DEGREES.) 



36 



(18 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 







9-489982 


6.48 


9-978206 


-68 


9-511776 


7-16 


10-488224 


60 


I 


490371 


6 


48 


978165 


-68 


512206 


7-16 


487794 


5^ 


2 


490759 


6 


2 


978124 


-68 


512635 


7-i5 


487365 


3 


491 147 


6 


978083 


.69 


5i3o64 


7-14 


486936 


57 


4 


491535 


6 


46 


978042 


-69 


513493 


7-14 


486507 


56 


5 


t^ 


6 


45 


978001 


-69 


513921 
514349 


7-i3 


486079 


55 


6 


6 


44 


977959 
977918 


-69 


7-i3 


485651 


54 


7 


SS; 


6 


44 


-69 


514777 


7-12 


485223 


53 


8 


6 


43 


977877 


.69 


5i52o4 


7-12 


484796 


52 


9 


493466 


6 


42 


977835 


.69 


5i563i 


7-11 


484369 


5i 


10 


493851 


6 


42 


977794 


-69 


516057 


7-10 


483943 


5o 


II 


9-494236 


6 


41 


9-977752 


-69 


9-516484 


7-10 


io-4835i6 


8 


12 


494621 


6 


41 


977711 


.69 


516910 


7-09 


483090 


i3 


495005 


6 


40 


977669 
977628 


-69 


517335 


7-09 


482665 


47 


14 


495388 


6 


39 


-69 


517761 


7-08 


482239 
48i8i5 


46 


i5 


493772 


6 


3o 

38 


977586 


-69 


5i8i85 


7-08 


45 


i6 


496154 


. 6 


977544 


■70 


518610 


7-07 


|og 


44 


17 


496537 


6 


37 


977503 


•70 


519034 


7-06 


43 


18 


496919 
497301 


6 


37 


977461 


■70 


519458 


7-06 


42 


19 


6 


36 


977419 


-70 


519882 


7-05 


480118 


41 


20 


497682 


6 


36 


977377 


-70 


52o3o5 


7-o5 


479695 


40 


21 


9-498064 


6 


35 


9-977335 


-70 


9-520728 


7-04 


10-479272 
478849 


39 


22 


498444 


6 


34 


977293 


•70 


52ii5i 


7-03 


38 


23 


498825 


6 


34 


977231 


-70 


521573 


7 -03 


478427 


37 


24 


499204 


6 


33 


977209 


• 70 


521995 


7-o3 


478005 


36 


25 


499384 


6 


32 


977167 


• 70 


522417 


7-02 


477583 


35 


26 


499963 


6 


32 


977125 


-70 


522838 


7-02 


477162 


34 


s 


5oo342 


6 


3i 


977083 


• 70 


523259 


7-01 


476741 


33 


500721 


6 


3i 


977041 


-70 


523680 


7-01 


476320 


32 


29 


to°;s? 


6 


3o 


976999 


• 70 


524100 


7-00 


475900 


3i 


3o 


6 


29 


976937 


•70 


524520 


6.99 


475480 


3o 


3i 


9-5oi854 


6 


11 


9.976914 
976872 


-70 


9-524939 


til 


10-475061 


11 


32 


5o223i 


6 




525359 


474641 


33 


502607 


6 


28 


976830 




525778 


6.^8 


474222 


27 
26 


34 


502984 
5o336o 


6 


27 


976787 




526197 


6.97 


4738o3 


35 


6 


26 


976745 




526615 


6.97 


473385 


25 


36 


503735 


6 


26 


976702 




527033 


6.96 


472967 
472349 


24 


U 


5o4iio 


6 


25 


976660 




527451 


6.96 


23 


504485 


6 


25 


976617 




527868 
528285 


6.95 


472132 


22 


39 


504860 


6 


24 


976574 




6.95 


471715 


21 


40 


5o5234 


6 


23 


976532 




528702 


6.94 


471298 


20 


41 


9 -505608 


6 


23 


9-976489 




'tint 


6.93 


10-470881 


\l 


42 


5o6354 


6 


22 


976446 




6.93 


470465 


43 


6 


22 


976404 




^SS 


6.93 


470o5o 


11 


44 


506727 


6 


21 


976361 




6.92 


469634 


45 


507099 


6 


20 


676318 




530781 


6.9, 


469219 

468804 


i5 


46 


507471 


6 


20 


976275 
976232 




53II96 


6.9, 


14 


s 


tf£ 


6 


19 




53i6u 


6.90 


468389 
467975 
467561 


13 


6 


\l 


976189 




532025 


6.90 
6.89 


12 


49 


5o8585 


6 


976146 




532439, 


II 


5o 


508956 


6 


18 


976103 




532853 


6.89 


467147 


10 


5i 


9.509326 


6 


17 


9-976060 




9.533266 


6.88 


10-466734 


i 


52 


5^S§ 


6 


16 


976017 




533679 


6.88 


466321 


53 


6 


16 


975974 




534092 


6.87 


465908 


1 


54 


510434 


6 


i5 


l]l&^ 




534304 


6-87 


465496 
465o84 


6 


55 


5io8o3 


6 


i5 




534916 


6-86 


5 


56 


511172 


6 


U 


975844 




535328 


6.86 


464672 


4 


57 


5ii54o 


6 


i3 


975800 




535739 


6.85 


464261 


3 


58 


511907 
512275 


6 


i3 


975757 




536 i5o 


6-85 


463850 


2 


59 


6 


12 


975714 
975670 




536561 


6.84 


463439 
463028 


1 


60 


512642 


6-12 




536972 


6-84 







Cosine 


D. 


Sine 


D. 


Cotang. 


D. 


Tang. 


M. 



(71 DEGEEES.) 



SINES AJND TANGENTS. (19 DEGEEES.) 



37 



M. 


Sine 


D. 


Cosiiie 


D. 


Tang. 


!>• 


Cotang. 







o-5l2642 


6..2 


9-975670 


^ 


9.536972 


6-84 


10.463028 


60 




5 1 3009 


6 


XX 


975627 


73 


537382 


6-83 


4626.8 


It 


2 


5i3375 


6 


XX 


975583 


H 


537792 


6-83 


462208 


3 


5i374i 


6 


xo 


97DD39 


73 


538202 


6-82 


461798 


57 


4 


514107 


6 


09 


975496 


^^ 


53861 X 


6-82 


46.389 


56 


5 


514472 


6 


09 


973432 


73 


539020 


6-8x 


460980 


55 


6 


514837 


6 


08 


975408 


73 


539429 


6-8x 


460371 


54 


7 


5i5202 


6 


08 


975363 


'^l 


539S37 


6-80 


460163 


53 


8 


5 1 5566 


6 


07 


975321 


73 


540245 


6-80 


459755 


52 


9 


5 1 5930 


6 


07 


975277 


73 


540653 


6-79 


499347 
408939 


5i 


10 


516294 


6 


06 


973233 


73 


54x061 


6-79 


5o 


II 


9 -516657 


6 


o5 


9.975x89 


^^ 


9.54x468 


6-78 


10-458532 


8 


12 


517020 


6 


05 


973x43 


73 


54x875 


6-78 


458x25 


i3 


517382 


6 


04 


975x01 


^^ 


542281 


6-77 


457719 


47 


U 


517745 


6 


04 


975057 


73 


542688 


6-77 


4573.2 


46 


i5 


518107 


6 


o3 


9750,3 


73 


543094 


6-76 


456906 


45 


i6 


518468 


6 


03 


974969 


74 


543499 


6.76 


45650 X 


44 


I? 


518829 


6 


02 


974923 


74 


543903 


6-75 


436095 


43 


i8 


519190 


6 


ox 


974880 


74 


5443x0 


6-75 


455690 
455285 


42 


19 


519551 


6 


01 


974836 


74 


544715 


6-74 


41 


20 


519911 


6 


00 


974792 


74 


545xx9 


6.74 


454881 


40 


21 


9-520271 


6 


00 


9.974748 


74 


9-545524 


6-73 


xo- 454476 


39 


22 


52063 1 


5 


99 


974703 


74 


543928 


6.73 


454072 


38 


23 


520990 


5 


99 


974659 


74 


54633 X 


6.72 


453669 

453263 


37 


24 


521349 


5 


98 


9746x4 


74 


546735 


6-72 


36 


25 


521707 


5 


98 


974570 


74 


547x38 


6.7X 


452862 


35 


26 


522066 


5 


97 


974525 


74 


547540 


6-7X 


402460 


34 


27 


522424 


5 


96 


974481 


74 


548345 


6-70 


432057 


33 


28 


522781 


5 


96 


974436 


74 


6-70 


45x655 


32 


29 


523.38 


5 


95 


974391 


74 


548747 


6-69 


45x253 


3i 


3o 


523495 


5 


95 


974347 


75 


549149 


6-69 


45o85i 


3o 


3i 


9-523852 


5 


94 


9-974302 


75 


9.549550 


6-68 


10 .450400 


11 


32 


524208 


5 


94 


974257 


75 


549951 


6-68 


450049 


33 


524564 


5 


93 


9742x2 


V 


55o352 


6-67 


449648 


11 


34 


524920 


5 


93 


974x67 


^^ 


550752 


6-67 


449243 


35 


525275 
525630 


5 


92 


974x22 


75 


551132 


6-66 


448848 


25 


36 


5 


91 


974077 


75 


55x552 


6-66 


448448 


24 


u 


520984 
526339 


5 


91 


974082 


75 


55x932 


6-65 


448048 


23 


5 


90 


973987 


75 


552351 


6-65 


447649 


22 


39 


526693 


5 


90 


973942 


73 


552750 


6-65 


447250 


2X 


40 


527046 


5 


89 


973897 


75 


553.49 


6-64 


446851 


20 


41 


9-527400 


5 


89 


9-973852 


75 


9-553548 


6-64 


X 0.44645 2 


19 


42 


527753 


5 


88 


973807 


75 


553946 


6-63 


446054 


18 


43 


528x05 


5 


88 


973761 


75 


554344 


6.63 


445656 


17 


44 


528458 


5 


87 


9737x6 


76 


55474X 


6.62 


445259 


16 


45 


528810 


5 


87 


973671 


76 


555x39 


6.62 


44486 X 


i5 


46 


529161 


5 


86 


973625 


76 


555536 


6.6x 


444464 


14 


8 


5295x3 


5 


86 


973580 


76 


555933 
556329 


6-61 


444067 


i3 


529864 


5 


85 


973535 


76 


6-60 


44367 X 


12 


49 


53o2x5 


5 


85 


973489 


76 


556725 


6-6o 


443275 


II 


5o 


53o565 


5 


84 


973444 


76 


557X2X 


6.59 


442879 


10 


5i 


9-53o9x5 


5 


84 


9-973398 


76 


9-5575x7 


6-59 


xo. 442483 


2 


52 


53x265 


5 


83 


973332 


76 


5579x3 


6-5o 


442087 


53 


53x6x4 


5 


82 


973307 


76 


5583o8 


6-58 


441692 


I 


54 


53x963 
5323x2 


5 


82 


97326X 


76 


558702 


6-58 


44x298 


55 


5 


8x 


9732x5 


76 


559097 


6-57 


440903 


5 


56 


532661 


5 


81 


973169 


76 


55949. 


6.57 


44o5o9 
4401 i5 


4 


57 


533009 


5 


80 


973124 


76 


559885 


6.56 


3 


58 


533357 


5 


80 


973078 


76 


560279 


6.56 


439721 


2 


59 


533704 


5 


7Q 


973o32 


77 


560673 


6.55 


439327 


I 


60 


534052 


5.78 


972986 


77 


56io66 


6.55 


438934 







Cosine 


D. 


Sine 


D. 


Cotan^. 


D. 


Tang. 


M. 



(70 DEGREES.) 



38 



(20 DEGREES.) A TABLE OF LOGAEITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 







9 -534032 


5.78 


9-972986 


•77 


g-56io66 


6-55 


10-438934 


60 


I 


534399 


5.77 


972940 


•77 


561459 


6-54 


438541 


5o 


2 


534745 


5.77 


972894 


•77 


56i85i 


6-54 


438149 


58 


3 


535092 
535438 


tVe 


972848 


•77 


562244 


6-53 


437756 


u 


4 


972802 


•77 


562636 


6-53 


437364 


5 


535783 


5-76 


972755 


•77 


563028 


6-53 


436972 
436581 


55 


6 


536129 


5-75 


972709 
972663 


•77 


563419 


6-52 


54 


I 


536474 


5-74 


•77 


563811 


6-52 


436189 


53 


5368 1 8 


5-74 


972617 


•77 


564202 


6-51 


435798 


52 


9 


537x63 


5-73 


972570 


•77 


564592 


6.5i 


435408 


5i 


10 


537507 


5-73 


972524 


•77 


564983 


6.5o 


435017 


5o 


II 


9-537851 


5-72 


9.972478 


•77 


9-565373 


6.5o 


10-434627 


49 


12 


538194 


5-72 


972431 


-78 


565763 


6.49 


434237 


48 


i3 


538538 


5-71 


972385 


.78 


5661 53 


6.49 


433847 


47 


14 


538880 


5.71 


972338 


.78 


566542 


6.49 


433458 


46 


i5 


539223 


5-70 


972291 


-78 


566932 


6.48 


433068 


45 


i6 


539565 


5-70 


972245 


■^l 


567320 


6.48 


432680 


44 


I? 


539907 


5-69 


972198 


■''I 


567709 


6.47 


432291 


43 


i8 


540249 


?:S 


972131 


■^^ 


568098 


6.47 


431902 


42 


19 


540590 


972105 


-78 


568486 


6-46 


43iDi4 


41 


20 


540931 


5-68 


972058 


-78 


568873 


6.46 


431127 


40 


21 


9-541272 


5-67 


9-972011 


-78 


9.569261 


6.45 


io-43o73g 


39 
3§ 


22 


54i6i3 


5-67 


971964 


•7^ 


569648 


6.45 


43o352 


23 


541953 


5-66 


971917 


•t 


570035 


6.45 


429965 


37 


24 


542293 


5-66 


971870 


•7^ 


570422 


6-44 


429378 


36 


25 


542632 


5-65 


971823 


-78 


570809 


6-44 


429191 


35 


26 


ItSVo 


5-65 


971776 


-78 


571195 


6-43 


428805 


34 


11 


5-64 


971729 


•79 


571581 


6-43 


428419 


33 


543649 


5-64 


971682 


•79 


571967 


6.42 


428033 


32 


29 


543987 
544325 


5-63 


971635 


■79 


572352 


6.42 


427648 


3i 


3o 


5-63 


971588 


•79 


572738 


6.42 


427262 


3o 


3i 


9-544663 


5-62 


9-971540 


■79 


9-573123 


6.41 


10-426877 


11 


32 


545000 


5-62 


971493 


•79 


573507 


6.41 


426493 


33 


545338 


5-6i 


971446 


•79 


573892 


6.40 


426108 


27 


34 


545674 


5-6i 


971398 


•79 


574276 


6.40 


425724 


26 


35 


54601 1 


5-60 


97I3D1 


•79 


574660 


6.39 


425340 


25 


36 


546347 


5.60 


97i3o3 


•79 


575044 


6.39 


424056 
424573 


24 


U 


546683 


5-59 


971256 


•79 


575427 


6.39 


23 


547019 




971208 


•79 


57D810 


6.38 


424190 


22 


39 


547354 


971161 


•79 


576193 


6.38 


423807 


21 


40 


547689 


5^58 


971113 


•79 


576576 


6.37 


423424 


20 


41 


9-548024 


5-57 


9-971066 


.80 


9-576908 
577341 


6.37 


io-423o4i 


;? 


42 


548359 
548693 


til 


971018 


-80 


6.36 


422659 


43 


970970 


-80 


577723 


6-36 


422277 


n 


44 


549027 


5-56 


970922 


-80 


578104 


6-36 


421896 


16 


45 


549360 


5-55 


970874 


-80 


578486 


6-35 


42i5i4 


i5 


46 


549693 


5-55 


970827 


-80 


578867 


6-35 


421133 


14 


S 


550026 


5-54 


970779 


-80 


579248 


6-34 


420752 


i3 


55o359 


5-54 


970731 


-80 


579629 


6.34 


420371 


12 


49 


550692 


5-53 


970683 


-80 


58ooog 


6.34 


419991 


II 


5o 


551024 


5-53 


970635 


• 80 


58o389 


6.33 


419611 


10 


5i 


9-55i356 


5-52 


9-970586 


.80 


9.580769 


6.33 


io-4i923r 


I 


52 


551687 
552018 


5-52 


970538 


.80 


581149 


6.32 


4i885i 


53 


5-52 


970490 


-80 


58i528 


6-32 


418472 


7 


54 


552349 


5-5i 


970442 


-80 


581907 


6-32 


418093 


6 


55 


552680 


5.5i 


970394 


-80 


582286 


6-31 


417714 


5 


56 


553010 


5-5o 


970345 


-81 


582665 


6.31 


417335 


4 


57 


553341 


5-50 


970297 


-81 


583043 


6.3o 


416957 


3 


58 


553670 


5-49 


970249 


-81 


583422 


6-3o 


416578 


2 


59 


554000 


5-49 


970200 


-81 


583800 


6-29 


416200 


I 


60 


554329 


5-48 


970152 


-81 


584.77 


6-29 


415823 







Cosine 


D. 


Sine 1 


D. 


Cotaiig. 


D. 


Tang. 


M. 



(69 DEGREES.) 



SINES AND TANGENTS. (21 DEGEEES.) 



39 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 







9-554329 


5-48 


9-970152 


81 


9 •5841 77 


6-29 


io-4i5823 


60 


I 


554658 


5.48 


970103 


81 


584555 


6 


29 


415445 


u 


2 


554987 


5.47 


970055 


81 


584982 
585309 


6 


28 


4i5o68 


3 


5553 1 5 


5-47 


970006 


8i 


6 


28 


414691 


57 


4 


555643 


5.46 


969957 


81 


585686 


6 


27 


414814 


56 


5 


555971 


5.46 


969909 


8i 


586062 


6 


27 


418088 
4i856i 


55 


6 


556299 


5.45 


969860 


81 


586489 


6 


27 


54 


7 


556626 


5.45 


96981 1 


81 


5868 1 5 


6 


26 


4i3i85 


53 


8 


556953 


5-44 


969762 


81 


58?566 


6 


26 


412810 


52 


9 


557280 


5-44 


969714 


81 


6 


25 


412484 


5i 


10 


557606 


5.43 


969665 


81 


587941 


6 


25 


412059 


5o 


II 


9.557932 


5.43 


9-969616 


82 


9-5888i6 


6 


25 


10-411684 


ii 


12 


558258 


5.43 


969567 


82 


588691 


6 


24 


411809 


i3 


558583 


5-42 


969518 


82 


589066 


6 


24 


410984 
4io56o 


47 


14 


558909 


5.42 


969469 


82 


589440 


6 


23 


46 


i5 


559234 


5-41 


969420 


82 


589814 


6 


28 


410186 


45 


i6 


559558 


5-41 


969370 


82 


590188 


6 


23 


409812 


44 


I? 


559883 


5-40 


969321 


82 


590562 


6 


22 


409488 


43 


i8 


560207 


5-40 


969272 


82 


590935 


6 


22 


409065 


42 


19 


56o53i 


5.39 


969223 


82 


591808 


6 


22 


408692 


41 


20 


56o855 


5.39 


969173 


82 


591681 


6 


21 


408819 


40 


21 


9.561178 


5-38 


9-969124 


82 


9-592054 


6 


21 


10-407946 
407574 


^1 


22 


56i5oi 


5.38 


969075 


82 


592426 


6 


20 


23 


561824 


5.37 


969025 


82 


592798 


6 


20 


407202 


37 


24 


562146 


5-37 
5-36 


968976 


82 


598170 


6 


19 


406829 


36 


20 


562468 


968926 


83 


598542 


6 


\l 


406458 


35 


26 


562790 


5-36 


968877 


83 


598914 


6 


406086 


34 


27 


563II2 


5.36 


968827 


88 


594285 


6 


18 


405715 


33 


28 


563433 


5.35 


968777 


88 


594656 


6 


18 


405344 


32 


?9 


563755 


5-35 


968728 


88 


595027 


6 


17 


404978 


3i 


3o 


564075 


5.34 


968678 


83 


595898 


6 


17 


404602 


3o 


3i 


9.564396 


5.34 


9-968628 


88 


9-595768 


6 


11 


iO'4o4232 


29 
28 


32 


564716 


5-33 


968578 


88 


596188 


6 


408862 


33 


565o36 


5.33 


96S528 


88 


596508 


6 


16 


408492 


27 


34 


565356 


5.32 


968479 


88 


596878 


6 


16 


408122 


26 


35 


565676 


5-32 


968429 


83 


597247 


6 


i5 


402753 


25 


36 


5663:4 


5.31 


968379 


83 


597616 


6 


i5 


402884 


24 


^7 


5.31 


968829 


83 


nut 


6 


i5 


4o20i5 


23 


38 


566632 


5.31 


968278 


83 


6 


14 


401646 


22 


39 


566951 


5.30 


968228 


84 


598722 


6 


14 


401278 


21 


40 


567269 


5-3o 


968178 


84 


599091 


6 


18 


400909 


20 


41 


9.567587 


5.29 


9-968128 


84 


9-599459 


6 


18 


io-4oo54i 


[I 


42 


567904 


5.29 


968078 


^^ 


599827 


6 


18 


400173 


43 


5682 2 2 


5.28 


968027 


84 


600194 


6 


12 


399806 


\l 


^ 


568539 


5.28 


967977 


84 


600062 


6 


12 


899438 


45 


568856 


5.28 


967927 


84 


600929 


6 


II 


398704 


i5 


46 


569172 


5.27 


967876 


84 


601296 
601662 


6 


II 


14 


47 


56948S 


5.27 


967826 


84 


6 


11 


898888 


i3 


48 


569804 


5.26 


967775 


84 


602029 
602895 
602761 


6 


10 


897971 


12 


P 


570120 


5.26 


967725 


84 


6 


10 


897605 


II 


5o 


570435 


5.25 


967674 


84 


6 


10 


397289 


10 


5i 


9.570751 


5-25 


9-967624 


84 


9-608127 
608498 


6 


09 


10-396878 


1 


52 


571066 


5-24 


967573 


84 


6 


09 


896507 


53 


57x380 


5-24 


967522 


85 


608808 


6 


2 


356142 


I 


l^ 


571695 


5.23 


967471 


85 


604228 


6 


895777 


5d 


572009 
572323 


5-23 


967421 


85 


604588 


6 


08 


3954.2 


5 


56 


5-23 


967870 


85 


604953 
6o53i7 


6 


07 


895047 


4 


s 


572636 


5-22 


967819 


85 


6 


07 


894688 


3 


572950 


5.22 


967268 


85 


6o5682 


6 


07 


894818 


2 


59 


573263 


5.21 


967217 


85 


606046 


6 


06 


398954 


I 


60 


573D75 


5.21 


967166 


85 


606410 


6-o6 


393590 





Cosine 


D. 


Sine 1 


dT 


Cotang. 


D. 


Tang. 


mT 



(68 DEGREES.) 



40 



(22 DEGREES.) A TABLE OF LOGARITHMIC 



M. 




Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 




^ 5?3888 


5.21 


9-967166 


.85 


9^606410 


6.06 


10 •393590 


60 


I 


5.20 


9671 i5 


• 85 


606773 


6 


06 


393227 


59 


2 


574200 


5.20 


967064 


.85 


607137 


6 


o5 


392863 


58 


3 


574512 


5.19 


967013 


-85 


607500 


6 


o5 


392500 


57 


4 


574824 


5.19 


966961 


-85 


607863 
608225 


6 


04 


392137 


56 


5 


575i36 


5.19 
5.i§ 


966910 


-85 


6 


04 


391775 


55 


6 


575447 


966809 
966808 


• 85 


6o8588 


6 


04 


391412 


54 


7 


575758 


5-18 


-85 


608950 
609312 


6 


o3 


391050 


53 


8 


576069 


^'7 


966756 


• 86 


6 


o3 


390688 


52 


9 


576379 


5.17 


966705 


-86 


609674 


6 


o3 


390326 
389964 


5i 


10 


576689 


5.16 


966653 


• 86 


6ioo36 


6 


02 


5o 


II 


'i]tl 


5.16 


9-966602 


■86 


9^6io397 
610759 


6 


02 


10-389603 


s 


12 


5.16 


966550 


•86 


6 


02 


389241 
388880 


i3 


577618 


5.i5 


966499 


• 86 


611120 


6 


01 


47 


14 


577927 


5-i5 


966447 


•86 


611480 


6 


01 


388520 


46 


i5 


578236 


5-14 


966395 


• 86 


611841 


6 


01 


388159 


45 


16 


578545 


5. ,4 


966344 


• 86 


612201 


6 


00 


387799 
387439 


44 


17 


578853 


5-13 


966292 


• 86 


6i256i 


6 


00 


43 


18 


579162 


5.13 


966240 


• 86 


612921 


6 


00 


387079 


42 


19 


579470 


5-13 


966188 


-86 


613281 


5 


99 


386719 


41 


20 


^19111 


5.12 


966136 


• 86 


6i364i 


5 


99 


386359 


40 


. 21 


9 -580085 


5.12 


9-966085 


• 87 


9-614000 


5 


98 


10-386000 


39 


22 


580392 


5. II 


966033 


•87 


614359 
614718 


5 


98 


385641 


38 


23 


580690 


5. II 


965981 


.87 


5 


98 


385282 


37 


24 


58ioo5 


5. II 


965928 
965876 


-87 


6i5o77 


5 


97 


384023 
384565 


36 


25 


58i3i2 


5.10 


•87 


61 5435 


5 


97 


35 


26 


58i6i8 


5.10 


965824 


-87 


615793 
6i6i5i 


5 


97 


384207 


34 


^l 


581924 


5.09 


965772 


-87 


5 


96 


383849 


33 


28 


582229 
582535 


5.09 


965720 


•87 


6i65o9 


5 


96 


383491 


32 


29 


1:2 


965668 


-87 


616867 


5 


96 


383i33 


3i 


3o 


582840 


9656 1 5 


•87 


617224 


5 


95 


3S2776 


3o 


3i 


9-583145 


5.08 


9-965563 


• 87 


9-617582 


5 


95 


10-382418 


29 


32 


583449 


5.07 


96551, 


•87 


617939 


5 


95 


382061 


28 


33 


583754 


5.07 


965458 


.87 


618295 


5 


94 


381705 


27 
26 


34 


584058 


5.06 


965406 


-87 


6i8652 


5 


94 


38i348 


35 


584361 


5.06 


965353 


• 88 


619008 


5 


94 


380992 


25 


36 


584665 


5.06 


965301 


• 88 


619364 


5 


93 


38o636 


24 


37 


584968 


5.o5 


965248 


• 88 


619721 


5 


93 


380279 


23 


38 


585272 


5.o5 


965195 


• 88 


620076 


5 


93 


379568 


22 


39 


585574 


5.04 


965143 


-88 


620432 


5 


92 


21 


40 


585877 


5.04 


965090 


-88 


620787 


5 


92 


379213 


20 


41 


9-586179 


5.o3 


9-965037 


• 88 


9-621142 


5 


92 


io^378858 


'9 


42 


586482 


5.o3 


964984 


• 88 


tiini 


5 


91 


378503 


18 


43 


586783 


5.o3 


^64031 
964879 
964826 


• 88 


5 


91 


378148 


17 


44 


587085 


5.02 


• 88 


622207 


5 


90 


377793 


16 


45 


587386 


5-02 


• 88 


622561 


5 


90 


^J7439 
377085 


i5 


46 


587688 


5-01 


964773 


• 88 


622915 


5 


% 


i4 


47 


587989 


5-01 


964719 


• 88 


623269 


5 


376731 


i3 


48 


588289 


5.01 


964666 


.89 


623623 


5 


89 


376377 


12 


49 


588590 


5.00 


964613 


-89 


623976 


5 


89 


376024 


n 


5o 


588890 


5.00 


964560 


• 89 


624330 


5 


88 


375670 


10 


5i 


'1^;?5 


4-99 


9-964507 


.89 


9 •624683 


5 


88 


io^3753i7 


I 


52 


4-99 


964454 


.89 


625o36 


5 


88 


374964 


53 


pa 


4-98 


964400 


.89 


625388 


5 


87 


374612 


I 


54 


964347 


.89 


625741 


5 


87 


374259 


55 


590387 


4.98 


964294 


.89 


626093 


5 


87 


373907 




56 


590686 


4-97 


964240 


-89 


626445 


5 


86 


373555 




s 


590984 


4-97 


964187 


• 89 


626797 


5 


86 


373203 




591282 


ill 


964133 


.89 


627149 


5 


86 


372851 




59 


591580 


964080 


.89 


627501 


5 


85 


372499 
37214S 




60 


591878 


4-96 


964026 


• 89 


627852 


5 85 







Cosine 


D. 


Sine 


D. 


Cotan^. 


D. 


Tang. 


"m7 



(67 DEGREES.) 



SINES AND TANGENTS. (23 DEGREES.) 



41 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 




o 


g. 591878 


4.96 


9-964026 


~^ 


9-627852 


5-85 


10-372148 


60 


I 


592176 


4-95 


963972 


.89 


62S203 


5-85 


371797 


S 


2 


592473 


4-95 


&,l 


.89 


628554 


5-85 


371446 


3 


592770 


4-93 


-90 


62S905 


5-84 


371095 


57 


4 


593067 


4.94 


96381 1 


-90 


629255 


5-84 


370745 


56 


5 


593363 


4-94 


963757 


• 90 


629606 


5-83 


370394 


55 


6 


093659 


4-93 


963704 


-90 


629956 


5-83 


370044 


54 


7 


593953 


4-93 


963650 


• 90 


63o3o6 


5-83 


369694 


53 


8 


594231 


4-93 


963596 


.90 


63o656 


5-83 


369344 


52 


9 


094547 


4-92 


963542 


-90 


63ioo5 


5-82 


368993 


5i 


10 


594842 


4.92 


963488 


.90 


63i355 


5-82 


368645 


5o 


II 


9.595137 


4-91 


9-963434 


-90 


9-631704 


5-82 


10-368296 


% 


12 


595432 


4-91 


963379 


.90 


632053 


5-81 


367947 


i3 


595727 


4-91 


963323 


-90 


632401 


5-81 


367399 


47 


14 


696021 


4-90 


963271 


-90 


632750 


5-81 


367230 


46 


10 


0963 1 5 


4-90 


963217 


.90 


633098 


5-80 


366902 


45 


i6 


596609 
596903 


4-89 


963 1 63 


.90 


633447 
633795 


5-8o 


366553 


44 


'7 


4-89 


963io3 


.91 


5-8o 


366205 


43 


i8 


597196 


4-89 


g63o34 


• 91 


634143 


5-79 


365857 


42 


19 


597490 


4-88 


962999 


.91 


634490 


5-79 


365510 


41 


20 


597783 


4-83 


962945 


-91 


634838 


5-79 


365i62 


40 


21 


9-598075 


4-87 


9-962890 
962836 


•91 


9-635x85 


5-78 


io-3648i5 


39 


22 


59S368 


4-87 


-91 


635532 


5-78 


364468 


38 


23 


598660 


4-87 


962781 


-91 


635879 


5-78 


364I2I 


37 


24 


598932 


4-86 


962727 


.91 


636226 


5-77 


363774 


36 


20 


599244 


4-86 


962672 


• 91 


636572 


5-77 


363428 


35 


26 


599336 


4-85 


962617 


•91. 


636919 


5-77 


363o8i 


34 


n 


599327 


4-85 


962362 


• 91 


637265 


5-77 


362735 


33 


28 


600118 


4-85 


962308 


.91 


63761 1 


5-76 


362389 


32 


?9 


600409 


4-84 


962453 


-91 


637956 
638302 


5-76 


362044 


3i 


3o 


600700 


4-84 


962398 


.92 


5-76 


361698 


3o 


3i 


9-600990 


4-84 


9-962343 


-92 


9-638647 


5.75 


io-36i353 


?? 


32 


601260 


4-83 


962288 


.92 


638992 


5-75 


361008 


U 


601570 


4-83 


962233 


.92 


639337 


5-75 


36o663 


27 


U 


601860 


4-82 


962178 


.92 


639682 


5-74 


36o3i8 


26 


35 


602 1 5q 


4-82 


962123 


.92 


640027 


5-74 


359973 


25 


36 


602439 


4-82 


962067 


.92 


640371 


5-74 


339629 


24 


.^T 


602728 


4-8i 


962012 


.92 


640716 


5-73 


359284 
358940 


23 


*38 


6o3oi7 


4-8i 


961957 


.92 


641060 


5-73 


22 


39 


6o33o5 


4-8i 


961902 


-92 


641404 


5-73 


358596 


21 


40 


603594 


4-8o 


961846 


-92 


641747 


5-72 


358233 


20 i 


4i 


9-6o3882 


4-8o 


9-961791 


-92 


9-642091 
642434 


5-72 


10-357909 




42 


604170 


4-79 


961735 


-92 


5-72 


357566 


18 


43 


604437 


4-79 


961680 


-92 


642777 


5-72 


357223 


17 


44 


604740 


V.l 


961624 


•93 


643120 


5-71 


356880 


16 


43 


6o5o32 


961569 


-93 


643463 


5-71 


336537 


i5 


46 


6o53i9 


4-78 


96i5i3 


•93 


643806 


5-71 


356.94 


U 


47 


6o56o6 


4-78 


961438 


•93 


644148 


5-70 


355852 


i3 


48 


605892 


4-77 


961402 


.93 


644490 
644832 


5-70 


355510 


12 


49 


606179 


4-77 


961346 


•93 


5-69 


355i68 


" i 


00 


606465 


4-76 


961290 


-93 


645174 


354826 


10 


5i 


9-606751 


4-76 


9-961235 


.93 


9-645516 


5.69 


10-354484 


I 


52 


607036 


4-76 


961179 
961123 


•93 


645857 


5.69 


354143 


53 


607322 


4-75 


-93 


646199 


i:§ 


353801 


7 


54 


607607 


4-75 


961067 


-93 


646540 


353460 


6 


55 


607892 


4-74 


961011 


-93 


646881 


5.68 


353119 


5 


56 


608177 


4-74 


960955 


-93 


647222 


5-68 


352778 




il 


608461 


4-74 


960899 


-93 


647562 


5.67 


352438 




58 


608745 


4-73 


960843 


.94 


647903 


5.67 


352097 




l^ 


609029 


4-73 


960786 


-94 


648243 


5-67 


351737 




6o 


609313 


4-73 


960730 


.94 


648583 


5-66 


35.417 






Cosine 


1 D. 


Sine 


D. 


Cotan?. 


D. 


Tang, i M. 



(66 DEGREES.) 



42 



(24 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 







9-6o93i3 


4-73 


9-960730 


94 


9-648583 


5-66 


10-351417 


60 


I 


609597 




72 


960674 


94 


648923 


5 


66 


351077 


f? 


2 


609880 




72 


960618 


94 


649263 


5 


66 


350737 


3 


610164 




72 


960561 


94 


649602 


5 


66 


350398 
35oo58 


57 


4 


610447 




71 


96o5o5 


94 


649942 


5 


65 


56 


5 


610729 




71 


960448 


94 


65o28i 


5 


65 


3497 '9 


55 


6 


611012 




70 


960392 
960335 


94 


65o62o 


5 


65 


349380 


54 


I 


611294 




70 


94 


650959 


5 


64 


349041 


53 


611576 




70 


960279 


94 


65i297 


5 


64 


348703 


52 


9 


6ii858 




69 


960222 


94 


65i636 


5 


64 


348364 


5i 


10 


612140 




69 


960165 


94 


651974 


5 


63 


348026 


5o 


II 


9-612421 




'& 


9-960109 


95 


9-652312 


5 


63 


10-347688 


s 


12 


612702 




960052 


95 


652650 


5 


63 


347350 


i3 


612983 




68 


959995 


95 


652988 


5 


63 


347012 


47 
46 


14 


613264 




67 


959938 


95 


653326 


5 


62 


346674 


i5 


613545 




67 


959882 


95 


653663 


5 


62 


346337 


45 


i6 


6i3825 




67 


959825 


95 


654000 


5 


62 


346000 


44 


17 


6i4io5 




66 


959768 


95 


654337 


5 


61 


345663 


43 


18 


614385 




66 


9597 1 1 


95 


654674 


5 


61 


345326 


42 


19 


614665 




66 


959654 


95 


655011 


5 


61 


344989 


41 


20 


614944 




65 


959596 


95 


655348 


5 


61 


344652 


40 


2? 


9-6i5223 




65 


9-939539 


95 


9-655684 


5 


60 


10-344316 


?? 


22 


6i55o2 


4 


65 


959482 


95 


656020 


5 


60 


343980 


23 


615781 




64 


959425 


95 


656356 


5 


60 


343644 


37 


24 


616060 




64 


959368 


95 


656692 


5 


59 


343308 


36 


25 


6i6338 




64 


959310 


96 


657028 


5 


59 


342972 


35 


26 


616616 




63 


959253 


96 


657364 


5 


59 


342636 


34 


27 


616894 


4 


63 


959195 


96 


657699 


5 


M 


342301 


33 


28 


617172 


. 


62 


09.38 


96 


658o34 


5 


341966 


32 


29 


617400 




62 


959081 


96 


658369 


5 


58 


34i63i 


3i 


3o 


617727 




62 


959023 


96 


658704 


5 


58 


341296 


3o 


3i 


9-618004 


4 


61 


9-958965 


96 


9-659039 


5 


58 


10-340961 


29 


32 


618281 


4 


61 


958go8 
958850 


96 


659373 


5 


57 


340627 


28 


33 


6i8558 




61 


96 


659708 


5 


57 


340292 
339958 


S 


34 


618834 




60 


958792 


96 


660042 


5 


57 


35 


619110 




60 


958734 


96 


660376 


5 


57 


339624 


25 


36 


619386 




60 


958677 


96 


660710 


5 


56 


339290 


24 


37 


619662 




59 


958619 


96 


661043 


5 


56 


338957 


23 


38 


619938 




59 


958561 


96 


661377 


5 


56 


338623 


22' 


39 


620213 




59 


9585o3 


97 


661710 


5 


55 


338290 
337957 


21 


40 


620488 




58 


958445 


97 


662043 


5 


55 


20 


41 


9-620763 




58 


9-958387 


97 


9-662376 


5 


55 


10-337624 


\l 


42 


621038 




57 


958329 


97 


662709 


5 


54 


3369^8 


43 


62i3i3 


4 


57 


958271 


97 


663042 


5 


54 


n 


44 


621587 




57 


958213 


97 


663375 


5 


54 


336625 


16 


45 


621861 




56 


9581 54 


97 


663707 


5 


54 


336293 


i5 


46 


622135 


4 


56 


958096 


97 


664039 


5 


53 


335961 


14 


47 


622409 


4 


56 


958o38 


97 


664371 


5 


53 


335629 


i3 


48 


622682 


4 


55 


957979 


97 


664703 


5 


53 


335297 


12 


49 


622956 


4 


55 


?^??63 


97 


665o35 


5 


53 


334965 


1 1 


5o 


623229 


4 


55 


97 


665366 


5 


52 


334634 


10 


5i 


9-623502 


4 


54 


9-957804 


97 


9-665697 


5 


52 


io.3343o3 


I 


52 


623774 




54 


957746 


98 


666029 


5 


52 


333971 


53 


624047 




54 


957687 
957628 


98 


666360 


5 


5i 


333640 


7 


54 


624319 




53 


98 


666691 


5 


5i 


333309 


6 


55 


624591 




53 


957570 


98 


667021 


5 


5i 


332979 
332648 


5 


56 


624863 




53 


95751 I 


98 


667352 


5 


5i 


4 


U 


625i35 




52 


957452 


98 


667682 


5 


5o 


3323i8 


3 


625406 




52 


957393 


98 


668013 


5 


5o 


331987 


2 


59 


625677 
625948 




52 


957335 


98 


668343 


5 


5o 


33i657 
33i328 


I 


60 


4-5i 


957276 


98 


668672 


5-5o 







Cosine 


D. 


Sine 


D. 


Cotangr. 


D. 


Tang. 


M. 



(65 DEGREES.) 



SINES AND TANGENTS. (25 DEGREES.) 



43 



M^ 


Sine 


D. i 


Cosine 


D. 1 


T;mg. 


D. ! 


Cotang. 







9.625948 


4-5i 


9.957276 


.93 


9.668673 


5-50 ' 


io-33i327 


60 


I 


626219 


4-5i 


957217 
957.58 


.98 


669002 


5-49 


330998 
330668 


U 


2 


626490 


4-5i 


.98 


669332 


5-49 


3 


626760 


4-5o 


957099 


.98 


669661 


5-40 


33o339 


57 


4 


627030 


4-5o 


957040 


.98 


669991 


5-48 


330009 


56 


5 


627300 


4-5o 


,5698> 


.98 


670320 


5-48 


329680 


55 


6 


627570 


4.49 


l&l 


•99 


670649 


5-48 


329351 


54 


7 


627840 


4.49 


•99 


670977 


5-48 


329023 
328694 


53 


8 


628109 
628378 


4-49 


956803 


•99 


67.306 


5-47 


52 


9 


4-48 


956744 


•99 


671634 


5.47 


328366 


5i 


10 


628647 


4.48 


956684 


•99 


671963 


5-47 


328037 


5o 


II 


9-628916 


4-47 


9.956625 


•99 


9.672291 


5-47 


10-327709 


a 


12 


629185 


4-47 


956566 


•99 


672619 


5.46 


32738. 


i3 


629453 


4-47 


9565o6 


•99 


672947 


5-46 


327053 


47 
46 


14 


629721 


4-46 


956447 


•99 


673274 


5-46 


326726 


i5 


629989 


4-46 


956387 


•99 


673602 


5.46 


326398 


45 


i6 


630257 


4.46 


956327 


•99 


673929 


5.45 


326071 


44 


n 


630324 


4-46 


956268 


•99 


674257 


5.45 


325743 


43 


iS 


630792 


4-45 


956208 


J. 00 


674584 


5.45 


325416 


42 


«9 


631039 


4-45 


956148 


1 .00 


6749.0 


5-44 


325090 


41 


20 


63i326 


4-45 


956089 


1. 00 


675237 


5.44 


324763 


40 


21 


9-631393 


4-44 


9.956029 


1. 00 


9.675564 


5.44 


10-324436 


ii 


22 


63 1 859 

632123 


4-44 


955969 


1. 00 


675890 


5-44 


324110 


23 


4-44 


gss 


1. 00 


676216 


5.43 


323784 


37 


24 


632392 


4-43 


1. 00 


676543 


5.43 


323457 


36 


25 


632638 


4-43 


955789 


1. 00 


676869 


5.43 


323.3. 


35 


26 


632923 


4-43 


955729 


1. 00 


677194 


5-43 


322806 


34 


27 


633189 


4-42 


955669 


1.00 


677520 


5-42 


322480 


33 


28 


633434 


4-42 


955609 


1. 00 


677846 


5-42 


322.54 


32 


29 


633719 


4-42 


955548 


1. 00 


678.71 


5.42 


32.829 


3i 


3o 


633984 


4-41 


955488 


1. 00 


678496 


5.42 


32i5o4 


3o 


3i 


9-634249 


4-41 


9.955428 


1. 01 


9-678821 


5.4. 


10-321179 


29 


32 


634514 


4-40 


955368 


I. 01 


679146 


5.41 


320854 


28 


33 


634778 


4-40 


955307 


1. 01 


679471 


5.41 


320329 


27 


34 


633042 


4.40 


955247 


J. 01 


679795 


5.41 


320205 


26 


35 


6353o6 


4-39 


955i86 


1. 01 


680120 


5.40 


319880 


25 


36 


635570 


4-39 


955126 


I. 01 


680444 


5.40 


319556 


24 


'^ 


635834 


til 


955o65 


1. 01 


680768 


5.40 


319232 


23 


636097 


955oo5 


1. 01 


681092 


5.40 


22 


39 


636360 


4-38 


954944 
954883 


I. 01 


6814.6 


5.39 


3 18584 


21 


40 


630623 


4-38 


I -01 


681740 


5.3^ 


318260 


20 


41 


9-636886 


4-37 


9.954823 


I-OI 


9-682063 


5-39 


10.317937 


19 


42 


637148 


4-37 


954762 


I-OI 


682387 


5-3o 


3176.3 


18 


43 


6374.1 


4-37 


954701 


l-OI 


682710 


5-38 


3.7290 


17 


44 


637,673 


4-37 


954640 


I-OI 


683o33 


5-38 


316967 


16 


45 


637935 


4-36 


954579 
934318 


I-OI 


683356 


5-38 


3.6644 


i5 


46 


6384^8 


4-36 


1.02 


683679 


5-38 


3i632i 


14 


47 


4-36 


954457 


1-02 


684001 


5.37 


3.5999 


i3 


48 


638720 


4-35 


954396 


1-02 


684324 


5.37 


3.5676 


12 


49 


638981 


4-35 


954335 


1.02 


684646 


5.37 


3.5354 


II 


5o 


639242 


4-35 


954274 


1.02 


684968 


5.37 


3.5o32 


ID 


5i 


9 -639503 


4-34 


9.954213 


1.02 


9-685290 


5.36 


io.3i47io 


1 


52 


639764 


4-34 


954152 


1.02 


6856.2 


5.36 


3.4388 


53 


640024 


4-34 


954090 


1.02 


685934 


5.36 


3.4066 


7 


54 


640284 


4-33 


954029 


1-02 


686255 


5.36 


3.3745 


6 


55 


640544 


4-33 


953968 


1.02 


686577 
686898 


5.35 


3 1 3423 


5 


56 


640804 


4-33 


^g23 


1.02 


5.35 


3.3.02 


4 


57 


641064 


4-32 


1.02 


687219 


5.35 


3.2781 


3 


58 


641324 


4-32 


953783 


1.02 


687540 


5.35 


3.2460 


2 


59 


641584 


4-32 


953722 


i.o3 


687861 


5.34 


3i2i39 
3ii8i8 


I 


60 


641842 


4-3i 


953660 


i.o3 


688182 


5-34 







Cosine 


D. 


Sine 


D. 


Cotang. 


D. 


Tansr. 


M. 



(64 DEGREES.) 



4A 



(26 DEGREES.) A TABLE OF LOGAEITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 







9-641842 


4-3i 


9-953660 


i-o3 


9-688182 


5-34 


io-3ii8i8 


60 


I 


642101 


4 


3i 


953599 


i-o3 


688502 


5 


34 


311498 


ll 


2 


642360 


4 


3i 


953537 


i-o3 


688823 


5 


34 


311177 


3 


642618 


4 


3o 


953475 


1-03 


689143 


5 


33 


3 10857 


57 


4 


642877 


4 


3o 


953413 


1-03 


689463 


5 


33 


3 1 0537 


56 


5 


643 1 35 


4 


3o 


953352 


i-o3 


689783 


5 


33 


310217 


55 


6 


643393 
643650 


4 


3o 


953290 


i-o3 


690103 


5 


33 


309897 


54 


7 


4 


29 


953228 


I -03 


690423 


5 


33 


309577 


53 


8 


643908 


4 


29 


953166 


i-o3 


690742 


5 


32 


309258 
308938 


52 


9 


644165 


4 


29 
28 


953104 


i-o3 


691062 


5 


32 


5i 


10 


644423 


4 


953042 


i-o3 


691381 


5 


32 


308619 


5o 


II 


9-644680 


4 


28 


9-952980 


1-04 


9-691700 


5 


3i 


io-3o83oo 


49 


12 


644936 


4 


28 


952918 
952855 


1-04 


692019 


5 


3i 


307981 


48 


i3 


645193 


4 


27 


1-04 


692338 


5 


3i 


307662 


47 


14 


645450 


4 


27 


902793 


1-04 


692656 


5 


3i 


307344 


46 


i5 


645706 


4 


27 


952731 


1-04 


692975 


5 


3i 


307025 


45 


i6 


645962 


4 


26 


952669 


1-04 


693293 


5 


3o 


306707 


44 


17 


646218 


4 


26 


952606 


1-04 


693612 


5 


3o 


3o6388 


43 


i8 


646474 


4 


26 


952544 


1-04 


693930 


5 


3o 


306070 


42 


19 


646729 


4 


25 


952481 


1-04 


694248 


5 


3o 


3o5752 


41 


20 


646984 


4 


25 


952419 


1-04 


694566 


5 


29 


3o5434 


40 


21 


9-647240 


4 


25 


9-952356 


1-04 


9-694883 


5 


29 


io-3o5ii7 


ll 


22 


647494 


4 


24 


952294 


1-04 


695201 


5 


29 


304799 


23 


647749 


4 


24 


952231 


1-04 


695518 


5 


29 


304482 


37 


24 


648004 


4 


24 


952168 


i-o5 


695836 


5 


29 


304164 


36 


25 


648258 


4 


24 


952106 


i-o5 


696153 


5 


28 


3o3847 


35 


26 


648512 


4 


23 


952043 


i-o5 


696470 


5 


28 


3o353o 


34 


27 


648766 


4 


23 


931980 


I -05 


696787 


5 


28 


3o32i3 


33 


28 


649020 


4 


23 


951917 


I -05 


697103 


5 


28 


302897 
3o258o 


32 


29 


649274 


4 


22 


951854 


i-o5 


697420 


5 


27 


3i 


3o 


649527 


4 


22 


95179' 


I -05 


697736 


5 


27 


302264 


3o 


3i 


9-649781 


4 


22 


9-951728 


I -05 


9-698053 


5 


27 


io.3oig47 


U 


32 


65oo34 


4 


22 


95i665 


i.o5 


698369 


5 


27 


3oi63i 


33 


650287 


4 


21 


951602 


i-o5 


69868D 


5 


26 


3oi3i5 


27 


¥. 


65o539 


4 


21 


951539 


i-o5 


699001 


5 


26 


IZlll 


26 


35 


650792 


4 


21 


951476 


i-o5 


699316 


5 


26 


25 


36 


651044 


4 


20 


951412 


i-o5 


699632 


5 


26 


3oo368 


24 


37 


65 1 297 


4 


20 


951349 


1-06 


699947 


5 


26 


3ooo53 


23 


38 


65 1 549 


4 


20 


951286 


1-06 


700263 


5 


25 


299737 


22 


39 


65 1800 


4 


19 


951222 


I -06 


700578 


5 


25 


299422 


21 


40 


652052 


4 


>9 


951159 


1-06 


700893 


5 


25 


299107 


20 


41 


9-6523o4 


4 


;? 


9-951096 
95io32 


1-06 


9-701208 


5 


24 


10-298792 


;§ 


42 


652555 


4 


1-06 


701523 


5 


24 


298477 


43 


652806 


4 


18 


950968 


1-06 


701837 


5 


24 


298163 


17 


44 


653o57 


4 


18 


$x 


I -06 


702152 


5 


24 


297848 


16 


45 


6533o8 


4 


18 


1-06 


702466 


5 


24 


297534 


i5 


46 


653558 


4 


'7 


950778 


1-06 


702780 


5 


23 


297220 


14 


47 


653So8 


4 


17 


950714 


1-06 


703095 


5 


23 


296905 


i3 


48 


654059 


4 


'7 


95o65o 


1-06 


703409 
703723 


5 


23 


296591 


12 


49 


654309 


4 


16 


95o586 


1-06 


5 


23 


296277 


II 


5o 


654558 


4 


16 


95o522 


1-07 


704036 


5 


22 


295964 


10 


5i 


9-654808 


4 


16 


9-950458 


1-07 


9-7o435o 


5 


22 


10-295650 


I 


52 


655o58 


4 


16 


950394 
95o33o 


1-07 


704663 


5 


22 


295337 


53 


655307 


4 


i5 


1-07 


704977 


5 


22 


295023 


7 


54 


655556 


4 


i5 


950266 


1.07 


705290 


5 


22 


294710 


6 


55 


655805 




i5 


950202 


1-07 


7o56o3 


5 


21 


294397 
294084 


5 


56 


656o54 




14 


95oi38 


1-07 


705916 


5 


21 


4 


57 


656302 




14 


950074 


1-07 


706228 


5 


21 


293772 


3 


58 


656551 




14 


950010 


1-07 


706541 


5 


21 


293459 


2 


59 


656799 




i3 


ms 


1-07 


706854 


5 


21 


293,46 


I 


60 


657047 


4-i3 


1-07 


707166 


5-20 


292834 







Cosine 


D. 


Sine 


D. 


Cotang. 


D. 


Tang. 


M. 



(63 DEGREES.) 



,.1 



SINES AND TANGENTS. (27 DEGREES.) 



45 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 







9-657047 


4-i3 


9-949881 


1-07 


9.707166 


5-20 


10.292834 


60 


I 


657295 


4-i3 


949816 


1-07 


707478 


5.20 


292522 


11 


2 


637542 


4-12 


949752 


1-07 


707790 


5.20 


292210 


3 


tUlT, 


4-12 


949688 


1-08 


708102 


5.20 


291898 


57 


4 


4-12 


949623 


i-o8 


708414 


5.19 


291586 


56 


5 


658284 


4-12 


949558 


I -08 


708726 


5.19 


291274 


55 


6 


658531 


4ii 


949494 


I -08 


709037 


5-19 


290963 


54 


I 


658778 


4-u 


949429 


I -08 


709349 


5-19 


290651 


53 


659025 


4-11 


949364 


I -08 


709660 


5.10 
5.1S 


290340 


52 


9 


639271 


4-10 


949300 


i-o8 


709971 


290029 


5i 


10 


639317 


4-10 


949235 


i-o8 


7x0282 


5-18 


289718 


5o 


II 


9.659763 


4-10 


9-949170 


I -08 


9.710593 


5.18 


10-289407 


ii 


12 


660009 


4-09 


949105 


I -03 


710904 


5-i8 


289096 
288785 


i3 


660255 


4-09 


949040 


1.08 


7ii2i5 


5.18 


47 


14 


66o5oi 


4-09 


948975 


I -08 


7II525 


5.17 


288475 


46 


i5 


660746 


4-oq 


^IS? 


I -08 


7II836 


5.17 


288164 


45 


i6 


660991 


4-o8 


1.08 


712146 


5.17 


287854 


44 


'7 


661236 


4-o8 


948780 


1-09 


712456 


5.17 


287544 


43 


i8 


661481 


4-o8 


948715 


1-09 


712766 


5.16 


287234 


42 


19 


661726 


4-07 


948650 


1-09 


'.llVsl 


5.16 


286924 


41 


20 


661970 


4-07 


948584 


1-09 


5.16 


286614 


40 


21 


9-662214 


4-07 


9-948519 


1-09 


9.713696 


5.16 


10-286304 


^2 


22 


662459 


4-07 


948454 


1-09 


714003 


5-16 


285995 


38 


23 


662703 


4-o6 


948388 


I -09 


714314 


5.i5 


285686 


37 


24 


662946 


4- 06 


948323 


1-09 


714624 


5.i5 


285376 


36 


23 


663190 


4-o6 


948257 


1-09 


714933 


5.i5 


285067 


35 


26 


663433 


4-o5 


948192 


1-09 


713242 


5.i5 


284758 


34 


27 


663677 


4-o5 


948126 


1-09 


7i555i 


5.14 


284449 


33 


28 


663920 


4-o5 


948060 


1-09 


7i586o 


5.14 


284140 


32 


29 


664163 


4-o5 


947995 


I-IO 


716168 


5.14 


283832 


31 


3o 


664406 


4-04 


947929 


I-IO 


716477 


5.14 


283523 


3o 


3r 


9-664648 


4-04 


9-947863 


I-IO 


9.716785 


5.14 


10-283215 


It 


32 


664891 


4-04 


947797 


I-IO 


717093 


5.i3 


282907 


33 


665 1 33 


4-o3 


947731 


I-IO 


717401 


5.i3 


282599 


27 


34 


665375 


4-o3 


947665 


I-IO 


717709 
718017 
718325 


5.i3 


282291 


26 


35 


665617 


4-o3 


947600 


I-IO 


5.i3 


281983 


25 


36 


665839 


4-02 


947533 


I-IO 


5.i3 


281670 


H 


37 


666100 


4-02 


947467 


I-IO 


718633 


5.12 


281367 


23 


38 


666342 


4-02 


947401 


I-IO 


718940 


5.12 


281060 


22 


39 


666583 


4-02 


947335 


I-IO 


719248 


5-12 


280752 


21 


40 


666824 


4-01 


947269 


I-IO 


719555 


5.12 


280445 


20 


41 


9-667065 


4-01 


9.947203 


I-IO 


9.719862 


5.12 


io.28oi38 


\l 


42 


667303 


4-01 


947136 


I - n 


720169 

720476 
720783 


5. II 


279831 


43 


667546 


4-ox 


947070 


I-II 


5. II 


279524 


17 


44 


667786 


4-00 


947004 


III 


5-11 


279217 


16 


45 


668027 


4-00 


946937 
946871 


I-II 


721089 


5. II 


278604 


i5 


46 


668267 


4-00 


I-II 


721396 


5-11 


14 


s 


668306 


3-99 


946804 


I-II 


721702 


5.10 


278298 


i3 


668746 


3-99 


946738 


I-II 


722009 
7223i5 


5.10 


277991 


12 


49 


668986 


3-99 


946671 


I-II 


5.10 


277685 


II 


5o 


669225 


3-99 


946604 


I-II 


722621 


5.10 


277379 


10 


5i 


9-669464 


3-98 


9-946538 


I-II 


9.722927 


5.10 


10-277073 


9 


52 


669703 


3-98 


946471 


I-II 


723232 


5.09 


276768 


8 


53 


669942 


3-98 


946404 


I-II 


723538 


5.09 


276462 


7 


54 


670181 


3.97 


946337 


I-II 


723844 


5.09 


276136 


6 


55 


670419 


3-97 


946270 


I-I2 


724149 


5.09 


275851 


5 


56 


670658 


3-97 


946203 


I - 12 


724434 


t:i 


275546 


4 


57 


670896 


3-97 


946 1 36 


I-I2 


]IUH 


275241 


3 


58 


671134 


3-^6 


946069 


I-I2 


5.08 


274935 


2 


59 


671372 


3.96 


946002 


I-I2 


725369 


5.08 


274631 


I 


60 


671609 


3.^6 


945935 


I-I2 


725674 


5.08 


274326 





Cosine 


D. 


Sine 


D. 


Cotanar. 


D. 


Tang. 


M. 



(62 DEGREES.) 



46 



(28 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 




o 


9-671609 


3.96 


9-945985 
945868 


I-I2 


9-725674 


5-08 


10-274826 


60 


I 


671847 


8 


95 


1-12 


725979 


5-08 


274021 


u 


2 


672084 


8 


95 


945800 


1-12 


726284 


5.07 


278716 


3 


672821 


8 


95 


945788 


1-12 


726588 


5-07 


278412 


57 


4 


672558 


3 


95 


945666 


I-I2 


726892 


5.07 


278108 


56 


5 


672795 
678032 


3 


94 


?gl? 


I-I2 


727197 


5.07 


272808 


55 


6 


3 


94 


I-I2 


727501 


5-07 


272499 


54 


7 


678268 


3 


94 


945464 


1-18 


727805 


5.06 


272195 


53 


8 


6785o5 


8 


94 


945896 


I-l3 


728109 


5-06 


271891 


52 


9 


678741 


8 


98 


945828 


i-i3 


728412 


5-06 


271588 


5i 


10 


678977 


3 


93 


945261 


1-18 


728716 


5-06 


271284 


5o 


II 


9-674218 


8 


93 


9-945198 


1-18 


9-729020 


5-06 


10-270980 


S 


12 


674448 


3 


92 


945'?5 


1-18 


729828 


5-o5 


270677 


i3 


674684 


3 


92 


945o58 


1-18 


729626 


5-o5 


270874 


47 


U 


674919 
675155 


8 


92 


944990 


1-18 


729929 


5-o5 


270071 


46 


i5 


8 


92 


944922 


1-13 


780233 


5-o5 


269767 


45 


i6 


675890 


8 


91 


944854 


1-18 


780535 


5-o5 


269465 


44 


17 


675624 


3 


91 


944786 


i-i3 


780888 


5-04 


269162 
268859 


43 


18 


675859 


3 


91 


944718 


i-i3 


781141 


5-04 


42 


19 


676094 


3 


91 


944650 


i-i8 


731444 


5-04 


268556 


41 


20 


676828 


3 


90 


944582 


I-I4 


731746 


5.04 


268254 


40 


21 


9-676562 


3 


90 


9-944514 


1-14 


9-782048 


5-04 


10-267952 


ll 


22 


676796 


3 


90 


944446 


1-14 


782851 


5-03 


267649 


23 


677080 


3 


^ 


944377 


I-I4 


782653 


5-o3 


267347 


37 


24 


677264 


8 


944309 


1-14 


782955 


5-08 


267045 


36 


25 


677498 


3 


f 


944241 


1-14 


788558 


5-08 


266748 


35 


26 


6777^1 


3 




944172 


I-I4 


5-08 


266442 


34 


27 


677964 


8 


88 


944104 


I -14 


788860 


5-02 


266140 


33 


28 


678197 


8 


88 


944036 


1-14 


784162 


5-02 


265888 


32 


29 


678480 


3 


88 


948967 


1-14 


784468 


5-02 


265587 


3i 


3o 


678668 


3 


88 


948899 


1-14 


784764 


5-02 


265236 


3o 


3i 


9-678895 


3 


87 


9-948880 


I-I4 


9-735o66 


5-02 


10-264934 


?l 


32 


679 > 28 


8 


87 


948761 


I -14 


785867 
735668 


5-02 


264688 


33 


679860 


3 


87 


948693 


i-i5 


5-01 


264882 


27 


34 


679592 


3 


87 


943624 


i-i5 


735969 


5-01 


264081 


26 


35 


t£U 


3 


86 


943555 


i-i5 


786269 


5-01 


268781 


25 


36 


3 


86 


948486 


i-i5 


786570 


5-01 


268480 


24 


37 


680288 


3 


86 


943417 


i-i5 


786871 


5-01 


268129 


23 


38 


68o5i9 


3 


85 


948848 


i-i5 


787171 


5-00 


262829 


22 


39 


680750 


8 


85 


948279 


i-i5 


787471 


5-00 


262529 


21 


40 


680982 


8 


85 


948210 


i-i5 


737771 


5-00 


262229 


20 


41 


9.681218 


8 


85 


9-948141 


i-i5 


9-738071 


5-00 


10-261929 


It 


42 


681448 


3 


84 


943072 


i-i5 


788871 


5-00 


261629 


43 


681674 


3 


84 


943008 


i-i5 


788671 


4-99 


261829 


17 


44 


681905 


3 


84 


• 942934 


i-i5 


788971 


4-99 


261029 


16 


45 


682185 


3 


84 


942864 


i-i5 


789271 


4-99 


260729 


i5 


46 


682865 


3 


88 


942795 


i-i6 


789570 


4-99 


260480 


14 


s 


682595 


8 


88 


942726 


1-16 


789870 


4-99 


260180 


i3 


682825 


8 


88 


942656 


i-i6 


740169 


4-99 


259881 


12 


49 


688055 


3 


88 


942587 


i-i6 


740468 


4-98 


259532 




5o 


688284 


3 


82 


942517 


i-i6 


740767 


4-98 


259238 


10 


5i 


9-6835i4 


3 


82 


9-942448 


i-i6 


9.741066 


4-98 


io-258g34 


I 


52 


688743 


3 


82 


942378 


i-i6 


741865 


4-98 


258635 


53 


688972 


3 


82 


942808 


i-i6 


741664 


4-98 


258336 


I 


54 


684201 


3 


81 


942289 


i-i6 


741962 


4-97 


258o88 


55 


684430 


3 


81 


942169 


I -16 


742261 


4-97 


257789 


5 


56 


684658 


3 


81 


942099 


i-i6 


742559 


4-97 


257441 


4 


57 


684887 
685ii5 


3 


80 


942029 


1-16 


742858 


4-97 


257142 


3 


58 


3 


80 


■ 941959 


I -16 


7481 56 


4-97 


256844 


2 


59 


685348 


3 


80 


941889 


1-17 


743454 


4-97 


256546 


I 


60 


685571 


3-80 


941819 


1-17 


748752 


4-96 


256248 







Cosine 


D. 


Sine 


D. 


Cotang. 


I). 


Tang. 1 M. | 



(61 DEGREES.) 



SINES AND TANGENTS. (29 DEGREES.) 



47 



M." 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cot;ing. j 





9.685571 


3.80 


9-941819 


1-17 


9'743752 


4-96 


10-236248 60 


I 


685799 


3-79 


94.749 


1-17 


744o5o 


4-96 


255950 59 

255632 58 


2 


686027 


3-79 


941679 


I-I7 


744348 


4-96 


3 


686254 


3-79 


941609 


I-I7 


744645 


4-96 


255355 1 57 


4 


686482 


3-79 
3-78 


94.539 


1-17 


744943 


4-96 


255o57 


56 


5 


686709 


941469 


1-17 


745240 


4-96 


234760 


55 


6 


686936 


3-78 


941398 


1-17 


745538 


4-95 


254462 


54 


I 


687163 


3-78 


941328 


I-I7 


745835 


4-95 


254.65 


53 


687389 


3-78 


941258 


1-17 


746.32 


4.95 


253868 


52 


9 


687616 


3-77 


941187 


1.17 


746429 


4-95 


253571 


5i 


10 


687843 


3-77 


941 1 17 


1. 17 


746726 


4-93 


253274 


5o 


II 


9.688069 


3-77 


9-941046 


1-18 


9-747023 


4.94 


10-252977 


49 


12 


688293 


3-77 


940975 


i-i8 


7473.9 


4.94 


232681 


48 


i3 


688521 


3-76 


940905 
940834 


I -18 


747616 


4-94 


232384 


47 


H 


688747 


3-76 


1-18 


747913 


4-94 


232087 


46 


i5 


688972 


3-76 


940763 


1-18 


748209 


4-94 


25.791 


45 


i6 


689.98 


3-76 


940693 


i-i8 


7485o5 


4.93 


25.495 


44 


17 


689423 


3-75 


940622 


1-18 


748801 


4-93 


230903 

25o6o7 


43 


i8 


689648 


3-75 


94055 I 


1-18 


749097 


4-93 


42 


19 


689873 


3-75 


940480 


1. 18 


7493q3 
749689 


4-93 


41 


20 


690098 


3-75 


940409 


i-i8 


4-93 


25o3.i 


40 


21 


9-690323 


3-74 


9-940338 


i-i8 


9-749985 


4-93 


.0-2500.5 


39 


22 


690548 


3-74 


940267 


i-i8 


750281 


4-92 


249719 


38 


23 


690772 


3-74 


940.96 


1-18 


750576 


4-92 


249424 


37 


24 


690996 


3-74 


940125 


I -19 


750872 


4-92 


249128 
248833 


36 


25 


691220 


3-73 


940054 


1-19 


731.67 


4-92 


35 


26 


691444 


3.73 


939982 


I -19 


751462 


4-92 


248538 


34 


27 


691668 


3.73 


9399.1 


1-19 


751757 


4-92 


248243 


33 


28 


69.892 


3-73 


939840 


1-19 


752052 


4-91 


247948 


32 


29 


6921.5 


3-72 


939768 


1-19 


752347 


4-91 


247653 


3i 


3o 


692339 


3-72 


939697 


1-19 


752642 


4-91 


247338 


3o 


3i 


9-692562 


3-72 


9-939625 


1-19 


9-752937 


4-91 


10-247063 


U 


32 


692785 


3-71 


939554 


1-19 


753231 


4-91 


246769 


33 


693008 


3.71 


939482 


1-19 


753526 


4-91 


246474 


11 


34 


69323. 


3.71 


9394.0 


1-19 


753820 


4.90 


246180 


35 


693453 


3.71 


939339 


1-19 


7541x5 


4.90 


245885 


23 


36 


693676 


3-70 


939267 


1-20 


754409 


4-90 


245591 


24 


37 


693898 


3-70 


939.95 


1-20 


754703 


4-90 


243297 


23 


38 


694120 


3-70 


939123 


1-20 


754997 


4-90 


245oo3 


22 


39 


694342 


3-70 


93S980 


1-20 


f5lH 


t% 


244709 
2444x5 


21 


40 


694564 


3-69 


1-20 


20 


41 


9-694786 


3-69 


9 -938908 


1-20 


9-755878 


4-89 


10-244.22 




42 


695007 


3.69 




1-20 


756172 
756465 


4-89 


2 ^3828 


43 


695229 


tu 


938763 


1-20 


4-89 


243535 


17 


44 


695450 


938691 


1-20 


756759 


4-89 


243241 


16 


45 


69567. 


3-68 


938619 


1-20 


757052 


4-89 


2429.48 
242655 


i5 


46 


695892 


3-68 


938547 


1-20 


757345 


4.88 


14 


s 


696.. 3 


3-68 


938475 


1-20 


757638 


4-88 


242362 


i3 


696334 


3.67 


938402 


I-2I 


757931 


^i^o 


242069 


12 


f^ 


696554 


3-67 


938330 


1-2. 


758224 


4-^? 


241776 
24x483 


1 1 


5o 


696775 


3-67 


938258 


I-2I 


7585x7 


4.88 


10 


5i 


9-696995 


3.67 


9-938.85 


I-2I 


9-7588x0 


4.88 


10-241190 


9 


52 


6972.3 


3-66 


938. .3 


I-2I 


759.02 


4-87 


240898 


8 


53 


697433 


3-66 


938040 


1-21 


]i^f, 


4-87 


240605 


7 


54 


697654 


3-66 


937967 


I. 21 


4-87 


24o3.3 


6 


55 


697874 


3-66 


937895 


I-2I 


759979 


4-87 


240021 


5 


56 


698094 


3-65 


937822 


I-2I 


760272 


4-87 


239728 


4 


ll 


6983.3 


3-65 


937749 


I-2I 


760564 


4-87 , 


239436 


3 


58 


698532 


3-65 


937676 


I-2I 


760856 


4-86 


239144 


2 


^ 


69875. 


3-65 


937604 


I-2I 


761 148 


4-86 


238352 


I 


60 


698970 


3.64 


937531 


I-2I 


761439 


4-86 


23856. 







Cosine 


D. 


Sine 


D. 


Cotans:. 


D. 


Tansr. 


~m7 



(60 DEGREES.) 



48 



(30 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine I 


). 


Tang. 


D. 


Cotang. 







9-698970 


3-64 


9-937531 I 


21 


9-761439 


4-86 


10-238561 


60 


I 


699189 


3 


64 


937458 I 


22 


76173. 


4-86 


238269 


u 


2 


699407 


3 


64 


937385 I 


22 


762023 


4-86 


237977 


3 


699626 


3 


64 


937312 1 


22 


762314 


4-86 


237686 


57 


4 


699844 


3 


63 


937238 I 


22 


762606 


4-85 


237394 


56 


5 


700062 


3 


63 


937165 I 


22 


762897 
763 1 88 


4-85 


237103 


55 


6 


700280 


3 


63 


937092 I 


22 


4-85 


2368.2 


54 


7 


700498 


3 


63 


937019 I 


22 


763479 


4-85 


236521 


53 


8 


700716 


3 


63 


llXt \ 


22 


763770 


4-85 


236230 


52 


9 


700933 


3 


62 


22 


764061 


4-85 


null 


5i 


10 


70ii5i 


3 


62 


936799 I 


22 


764352 


4-84 


5o 


II 


9-701368 


3 


62 


9-936725 I 


22 


9-764643 


4-84 


10-235357 


§ 


12 


701585 


3 


62 


936652 I 


23 


764933 


4-84 


235067 


i3 


701802 


3 


61 


936578 I 


23 


765224 


4-84 


234486 


47 


U 


702019 


3 


61 


9365o5 I 


23 


765514 


4-84 


46 


i5 


702236 


3 


61 


936431 I 


23 


7658o5 


4-84 


234195 


45 


i6 


702452 


3 


61 


936357 I 


23 


766095 


4-84 


233905 


44 


17 


702669 


3 


60 


936284 I 


23 


766385 


4-83 


2336.5 


43 


18 


702885 


3 


60 


936210 I 


23 


766675 


4-83 


233325 


42 


19 


7o3ioi 


3 


60 


936i36 I 


23 


766965 


4-83 


233o35 


41 


20 


7033x7 


3 


60 


936062 I 


23 


767255 


4-83 


232745 


40 


21 


9.703533 


3 


59 


9-935988 I 


23 


9-767545 


4-83 


10-232455 


12 


22 


703749 


3 


59 


935914 I 


23 


767834 


4-83 


232.66 


23 


703964 


3 


59 


935840 I 


23 


768124 


4-82 


23.876 


37 


24 


704395 


3 


59 


935766 I 


24 


768413 


4-82 


23.587 


36 


25 


3 


it 


935692 I 


24 


768703 


4-82 


23.297 


35 


26 


704610 


3 


935618 I 


24 


&: 


4-82 


23.008 


34 


27 


704825 


3 


58 


935543 I 


24 


4-82 


230719 


33 


28 
29 


7o5o4o 
705254 


3 
3 


58 
58 


935469 1 
935396 I 


24 
24 


769570 
769860 


4-82 
4-8i 


23o43o 
23oi4o 


32 

3i 


3o 


705469 


3 


57 


935320 1 


24 


770148 


4-8i 


22q852 


3o 


3i 


9-705683 


3 


57 


9-935246 I 


24 


9-770437 


4-8i 


10.229563 


^? 


32 


705898 


3 


57 


935.71 I 


24 


770726 


4-8i 


229274 
228985 


28 


33 


7061 12 


3 


57 


935097 I 


24 


7710.5 


4-8i 


27 


34 


706326 


3 


56 


935022 I 


24 


77i3o3 


4-8i 


228697 


26 


35 


706539 


3 


56 


934948 I 


24 


77.592 


4-8i 


228408 


25 


36 


706753 


3 


56 


934873 I 


24 


77.880 


4-8o 


228.20 


24 


37 


706967 


3 


56 


934798 I 


25 


772.68 


4-8o 


227832 


23 


38 


707 1 So 


3 


55 


934723 I 


25 


772457 


4-8o 


227543 


22 


39 


707393 


3 


55 


934649 I 


25 


772745 


4-80 


227255 


21 


40 


707606 


3 


55 


934574 I 


25 


773o33 


4-8o 


226967 


20 


41 


9.707819 


3 


55 


9.934499 I 


25 


9-77332. 


4-8o 


10.226679 


;? 


42 


708032 


3 


54 


934424 I 


25 


773608 


4-79 


226392 


43 


708245 


3 


54 


934349 I 


25 


773896 
774184 


4-79 


226104 


\i 


44 


708458 


3 


54 


934274 I 


25 


4-79 


2258.6 


45 


708670 


3 


54 


934.99 1 
934123 I 


25 


774471 


4-79 


225529 


i5 


46 


708882 


3 


53 


25 


774759 


4-79 


22524. 


'i 


47 


709094 


3 


53 


934048 I 


a5 


775046 


4-79 


224954 


i3 


48 


709306 


3 


53 


933073 I 


25 


775333 


4-79 


224667 


12 


49 


709518 


3 


53 


933898 I 


26 


77562. 


4-78 


224379 


II 


5o 


709730 


3 


53 


933822 I 


26 


775908 


4-78 


224092 


10 


5i 


9-709941 


3 


52 


9-933747 I 


26 


9-776195 


4-78 


io.2238o5 


I 


52 


710153 


3 


52 


933671 I 


26 


776482 


4-78 


2235.8 


53 


7io364 


3 


52 


933596 1 


26 


776769 
777053 


4-78 


22323. 


7 


54 


710575 


3 


52 


933520 I 


26 


4-78 


222945 


6 


55 


710786 


3 


5i 


933445 I 


26 


777342 


4-78 


222658 


5 


56 


710997 


3 


5i 


933369 I 


26 


777628 


4-77 


222372 


4 


11 


711208 


3 


5i 


933293 I 


26 


777915 


4-77 


222085 


3 


711419 


3 


5i 


933217 1 


26 


778201 


4-77 


22.799 


2 


59 


711629 


3 


5o 


933141 I 


26 


778487 


4-77 


22.5.2 


I 


60 


711839 


3-50 


933066 I 


26 


778774 


4-77 


22.226 







Cosine 


D. 


Sine T 


). 


Cotaner. 


D. 


Tang. |M. 



(59 DEGREES.) 



SINES AND TANGENTS. (31 DEGREES.) 



49 



M. 


Sine 


D. 1 


Cosine 


D. 


Tang. 


D. 


Cotang. 







9.7U839 


3-5o 


9 -933066 


1-26 


9-778774 


4-77 


10-221226 


60 


I 


712030 


3-5o 


932990 


1-27 


779060 


4-77 


22og4o 


It 


2 


712260 


3.5o 


932^38 


1-27 


779346 


4-76 


220654 


3 


712469 


3-49 


1-27 


779632 


4-76 


220368 j 57 1 


4 


712679 


3-49 


932762 


1.27 


7799'8 


4-76 


220082 


56 


5 


712889 


3-49 


932685 


1-27 


780203 


4-76 


219797 


55 


6 

I 


71-3098 

7i33o8 


3-49 
3-49 


lilts 


1-27 

1-27 


780489 
780775 


4-76 
4-76 


219511 
219225 
218940 


54 
53 


713517 


3-48 


932457 


1-27 


781060 


4-76 


52 


9 


713726 


3-48 


932380 


1-27 


781346 


4-75 


218654 


5i 


10 


713935 


3-48 


932304 


1-27 


781631 


4-75 


218369 


5o 


II 


9-714144 


3-48 


9-932228 


1-27 


9-781916 


4-75 


10-218084 


49 


12 


714352 


3-47 


93-3 i5i 


1-27 


782201 


4-75 


217799 


48 


i3 


714561 


3-47 


932075 


1-28 


782486 


4-75 


2,75.4 


47 


14 


714769 


3-47 


931998 


1-28 


782771 


4-75 


217229 


46 


i5 


71497a 


3-47 


931021 
931843 


1-28 


783o56 


4-75 


216944 


45 


i6 


7i5i86 


3-47 


1-28 


783341 


4-75 


216659 


44 


I? 


715394 


3-46 


931768 


1-28 


783626 


4-74 


216374 


43 


i8 


7i56o2 


3-46 


931691 


1-28 


783910 


4-74 


216090 


42 


19 


715809 


3-46 


931614 


1-28 


784195 


4-74 


2i58o5 


41 


20 


716017 


3-46 


93 1 537 


1.28 


784479 


4-74 


215521 


40 


21 


9-716224 


3-45 


9.931460 


1-28 


9-784764 


4-74 


io-2i5236 


11 


22 


716432 


3.45 


93 1 383 


1-28 


785048 


4-74 


214952 


23 


716639 


3.45 


93i3o6 


1-28 


785332 


4-73 


214668 


u 


24 


716846 


3-45 


93 1 229 


1-29 


7856 I 6 


4-73 


214384 


25 


717053 


3.45 


93ii52 


1-29 


785900 


4-73 


214100 


35 


26 


717259 


3-44 


931075 


1.29 


786184 


4-73 


2i38i6 


34 


27 


717466 


3-44 


930998 


1-29 


786468 


4-73 


213532 


33 


28 


717673 


3-44 


930921 
930843 


1-29 


786752 


4-73 


213248 


32 


2g 


717879 


3-44 


1-29 


787036 


4-73 


212964 


3i 


3o 


718085 


3-43 


930766 


1-29 


787319 


4-72 


212681 


3o 


3i 


9-718291 


3.43 


9-930688 


1-29 


9.787603 


4-72 


10-212397 


29 
28 


32 


718497 


3-43 


930611 


1-29 


787886 


4-72 


212114 


33 


718703 


3-43 


93o533 


1-29 


788170 


4-72 


2ii83o 


27 


34 


718909 


3.43 


93o456 


1-29 


788453 


4-72 


211547 


26 


35 


719114 


3-42 


930378 


1-29 


788736 


4-72 


211264 


25 


36 


719320 


3.42 


93o3oo 


1-30 


789019 


4-72 


210981 


24 


37 


71952D 


3-42 


930223 


I -30 


789302 


4-71 


210698 


23 


38 


719730 


3-42 


930145 


i-3o 


789585 


4-71 


2io4i5 


22 


39 


719935 


3-41 


930067 


1-30 


789868 


4-71 


2IOl32 


21 


40 


720140 


3-41 


929989 


i-3o 


790i5i 


4-71 


209849 


20 


4i 


9-720345 


3-41 


9-929911 
929833 


1-30 


9-790433 


4-71 


10-209567 


\l 


42 


720549 


3-41 


i-3o 


790716 


4-71 


209284 


43 


720754 


3-40 


929755 


1. 30 


790999 


4-71 


209001 


17 


44 


720958 


3-40 


929677 


i-3o 


791281 


4-71 


208719 


16 


45 


721162 


3-40 


929599 


1-30 


791563 


4-70 


208437 


i5 


46 


721366 


3-40 


929321 


i-3o 


791846 


4-70 


208154 


14 


47 


721570 


3-40 


929442 


i-3o 


792128 


4-70 


207872 


i3 


48 


721774 


3.39 


929364 


i-3i 


792410 


4-70 


207590 


12 


f^ 


721978 


3-39 


929286 


i-3i 


792692 


4-70 


207308 


II 


5o 


722181 


3-39 


929207 


1-31 


792974 


4-70 


207026 


10 


5i 


9-722385 


3-39 


9-929129 


i-3i 


9-793256 


4-70 


10-206744 


9 


52 


722588 


3.39 


929050 


i-3i 


793538 


4-69 


206462 


8 


53 


722791 


3-38 


IZI 


i-3i 


793819 


4-69 


206I8I 


7 


54 


722994 


3-38 


1-31 


794101 


4-69 


205899 


6 


55 


723197 


3-38 


928815 


i.3i 


794383 


4-69 


2o56i7 


5 


56 


723400 


3-38 


928736 


i-3i 


794664 


4-69 


205336 


4 


^o 


723603 


3.37 


928657 


i-3i 


794945 


4-69 


2o5o55 


3 


58 


7238o5 


3-37 


928578 


i-3i 


]& 


4-68 


204773 


2 


59 


724007 


3.37 


928499 


i-3i 


204492 


I 


6o 


724210 


3-37 


928420 


i-3i 


795789 


4-68 


2042 1 1 







1 Cosine 


D. 


Sine 


D. 


Cotang. 


D. 


1 Tang. 



(58 DEGREES.) 



50 



(32 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 







9-724210 


3.37 


9-928420 


1-32 


9-795789 


4-68 


10-204211 


60 


I 


724412 


3.37 


928342 


1-32 


tTr 


4-68 


203930 


ii 


2 


724614 


3-36 


928263 


1-32 


4-68 


203649 


3 


724816 


3-36 


928183 


1-32 


796632 


4-68 


203368 


u 


4 


725017 


3-36 


928104 


1-32 


7969:3 


4-68 


203087 


5 


725219 


3-36 


928025 


1-32 


797194 


4-68 


202806 


55 


6 


725420 


3-35 


927946 


1-32 


797473 


4-68 


202525 


54 


7 


725622 


3-35 


927867 


1-32 


797755 


4-68 


202245 


53 


8 


725823 


3-35 


927787 
927708 


1-32 


798036 


4-67 


201964 


52 


9 


726024 


3-35 


1-32 


7983:6 


4-67 


20:684 


5i 


10 


726225 


3-35 


927629 


1-32 


798596 


4-67 


20:404 


5o 


II 


9-726426 


3.34 


9-927549 


1-32 


9-798877 


4-67 


IO-20II23 


% 


12 


726626 


3-34 


927470 


:-33 


799:57 


4-67 


200843 


i3 


726827 


3-34 


927390 


:-33 


799437 


4-67 


200563 


47 
46 


U 


727027 


3.34 


927310 


1-33 


799717 


ttl 


200283 


i5 


727228 


3.34 


927231 


1-33 


799997 


2oooo3 


45 


i6 


727428 


3-33 


927.51 


1-33 


800277 


4-66 


199723 


44 


\l 


727628 


3-33 


927071 


1-33 


800557 


4-66 


199443 


43 


727828 


3-33 


926991 


1-33 


8oo836 


4-66 


I98884 


42 


19 


728027 


3-33 


9269.1 


1-33 


8o:::6 


4-66 


41 


20 


728227 


3-33 


926831 


1-33 


80:396 


4-66 


198604 


40 


21 


9-728427 


3-32 


9-926751 


1-33 


9-801675 
80:955 


4-66 


10-198325 


39 
38 


22 


728626 


3-32 


926671 


1-33 


4-66 


198045 


23 


728825 


3-32 


926591 


1-33 


802234 


4-65 


197766 


37 


24 


729024 


3-32 


9265ii 


1-34 


8o25i3 


4-65 


197487 


36 


25 


729223 


3-3i 


926431 


1-34 


802792 


4-65 


197208 


35 


26 


729422 


3-3i 


92635: 


:-34 


803072 


4-65 


196928 


34 


27 


729621 


3-3i 


926270 


:-34 


8o335i 


4-65 


196649 


33 


28 


729820 


3-3i 


926:90 


:-34 


8o363o 


4-65 


196370 


32 


29 


730018 


3-3o 


926::o 


1-34 


803908 


4-65 


196092 


3i 


3o 


730216 


3-3o 


926029 


1-34 


804:87 


4-65 


1958.3 


3o 


3i 


9-7304.5 


3-3o 


'■??§§ 


'Ji 


9-804466 


4-64 


10-195534 


11 


32 


7306.3 


3-3o 


804745 


4-64 


195255 


33 


730811 


3-3o 


925788 


1-34 


8o5o23 


4-64 


194977 


27 


34 


73:009 


3-29 


925707 


1-34 


8o53o2 


4-64 


194698 


26 


35 


73.206 


3-29 


925626 


1.34 


8o558o 


4-64 


194420 


25 


36 


73.404 


3-29 


925545 


1-35 


8o5859 


4-64 


194.41 


24 


37 


73.602 


3-29 


925465 


:-35 


806:37 


4-64 


193863 


23 


38 


73.799 


3-29 


925384 


1-35 


8064: 5 


4-63 


193535 


22 


39 


73.996 


3-28 


9253o3 


1-35 


806693 


4-63 


193307 


21 


40 


732193 


3-28 


925222 


:-35 


806971 


4-63 


193029 


20 


41 


'■&'^ 


3-28 


9-925:41 


:-35 


9-807249 


4-63 


10-19275: 


'9 


42 


3-28 


925o6o 


:.35 


807527 


4-63 


:92473 


:8 


43 


732784 


3-28 


924979 
924897 


1-35 


807805 


4-63 


:92:95 


17 


44 


732980 


3-27 


1-35 


808083 


4-63 


191917 


16 


45 


733.77 


3-27 


9248:6 


1-35 


8o836: 


4-63 


:9:639 


i5 


46 


733373 


3-27 


924735 


1-36 


8o8638 


4-62 


:9:362 


14 


47 


733569 


3-27 


924654 


:-36 


8089:6 


4-62 


:9:o84 


:3 


48 


733760 


3-27 


924572 


:-36 


809:93 


4-62 


190807 


:2 


49 


733961 


3-26 


924491 


1-36 


809471 


4-62 


190529 


II 


5o 


734.57 


3-26 


924409 


1-36 


809748 


4-62 


190252 


10 


5i 


9-734353 


3.26 


9-924328 


1-36 


9-8:0025 


4-62 


:o- 189975 


I 


52 


734549 


3-26 


924246 


1-36 


8:o3o2 


4-62 


: 89698 


53 


734744 


3-25 


924:64 


1-36 


8io58o 


4-62 


189420 


7 


54 


?MS 


3-25 


924083 


■ :-36 


8:0857 


4-62 


189:43 


6 


55 


3-25 


92400: 


1-36 


8::i34 


4-6: 


188866 


5 


56 


735330 


3-25 


9239:9 


1-36 


8::4io 


4-6: 


188590 


4 


57 


735525 


3-25 


923837 


1-36 


8::687 


4-61 


i883:3 


3 


58 


7357.9 


3-24 


923755 


1-37 


8::964 


4-6i 


i88o36 


2 


59 


7359.4 


3.24 


923673 


1.37 


8:2241 


4-61 


187759 
187483 


I 


60 


736109 


3.24 


923591 


1-37 


8:25:7 


4-61 







Cosine 


D. 


Sine 


D. 


Cotanar. 


D. 


Tang. 


IT 



(5Y DEGREES.) 



SINES AKD TANGENTS. (33 DEGREES.) 



51 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 





9.736109 


3.24 


9.923591 


1.37 


9-812517 


4-bi 


10-187482 60 


I 


7363o3 


3 


24 


923509 


1.37 


812794 


4 


61 


187206 59 
186930 ! 58 


2 


736498 


3 


24 


923427 


1.37 


813070 


4 


61 


3 


?S£ 


3 


23 


923345 


1.37 


813347 
8i3623 


4 


60 


186653 


a 


4 


3 


23 


923263 


1.37 


4 


60 


186377 


5 


737080 


3 


23 


923181 


1.37 


813899 
814175 


4 


60 


186101 


55 


6 


737274 


3 


23 


923098 


1.37 


4 


60 


185825 


54 


7 


737467 


3 


23 


923016 


1.37 


8,4452 


4 


60 


185548 


53 


8 


737661 


3 


22 


922^51 


1.37 


&14728 


4 


60 


185272 


52 


9 


?as 


3 


22 


\:U 


8i5oo4 


4 


60 


184996 


5i 


10 


3 


22 


922768 


815279 


4 


60 


184721 


5o 


II 


9.738241 


3 


22 


9.922686 


1.38 


9.815555 


4 


59 


10-184445 


g 


12 


738434 


3 


22 


922603 


1.38 


8i583i 


4 


59 


184169 
183893 


i3 


738627 


8 


21 


922520 


1.38 


816107 


4 


59 


47 


U 


738820 


3 


21 


922438 


1.38 


8i6382 


4 


59 


i836i8 


46 


i5 


739013 


3 


21 


922355 


1.38 


8 16658 


4 


59 


183342 


45 


i6 


739206 


3 


21 


922272 


1.38 


816933 


4 


59 


183067 


44 


n 


739398 


3 


21 


922189 


1-38 


817209 


4 


59 


182791 


43 


i8 


]^Ts 


3 


20 


922106 


1-38 


817484 


4 


59 


i825i6 


42 


19 


3 


20 


922023 


1-38 


l\illl 


4 


it 


182241 


41 


20 


739975 


3 


20 


921940 


1.38 


4 


181965 


40 


21 


9.740167 


3 


20 


9.921857 


1.39 


9-8i83io 


4 


58 


10-181690 


ll 


22 


740359 


3 


20 


921774 


1.39 


8i8585 


4 


58 


i8i4i5 


23 


74o55o 


3 


19 


921691 


1.39 


818860 


4 


53 


181140 


37 


24 


740742 


3 


19 


921607 


1.39 


819135 


4 


58 


180865 


36 


25 


740934 


3 


19 


921524 


1.39 


819410 


4 


58 


180590 


35 


26 


741 1 25 


3 


19 


921441 


1.39 


819684 


4 


58 


i8o3i6 


34 


27 


74i3i6 


3 


;? 


921357 


1.39 


819959 


4 


58 


180041 


33 


28 


741 5o8 


3 


921274 


1.39 


820234 


4 


58 


179766 


32 


29 


741699 


3 


18 


921190 


1.39 


82o5o8 


4 


57 


179492 


3i 


3o 


741889 


3 


18 


921107 


1.39 


820783 


4 


57 


179217 


3o 


3i 


9.742080 


3 


18 


9.921023 


1.39 


9.821057 


4 


57 


10-178943 


3 


32 


742271 


3 


18 


'au 


1.40 


821332 


4 


57 


178668 


33 


742462 


3 


17 


1-40 


821606 


4 


57 


178394 


S 


34 


742652 


3 


17 


920772 


1.40 


821880 


4 


57 


178120 


35 


742842 


3 


17 


920688 


1.40 


822154 


4 


57 


177846 


25 


36 


743o33 


3 


17 


920604 


1.40 


822429 


4 


57 


177571 


24 


37 


743223 


3 


17 


920520 


1.40 


822703 


4 


57 


177297 


23 


38 


743413 


3 


16 


920436 


1-40 


822977 


4 


56 


177023 


22 


39 


743602 


3 


16 


920352 


1.40 


823250 


4 


56 


176750 


21 


40 


743792 


3 


16 


920268 


1.40 


823524 


4 


56 


176476 


20 


41 


9.743982 


3 


16 


9.920x84 


1-40 


9.823798 


4 


56 


10-176202 


;? 


42 


7441 7 I 


3 


16 


920099 
920015 


1.40 


824072 


4 


56 


175928 


43 


744361 


3 


i5 


1.40 


824345 


4 


56 


175655 


u 


44 


744550 


3 


i5 


919846 


1. 41 


'& 


4 


56 


175381 


45 


744739 
744928 


3 


i5 


1. 41 


4 


56 


175107 


i5 


46 


3 


i5 


919762 


1. 41 


825166 


4 


56 


174834 


14 


47 


745117 


3 


i5 




1. 41 


825439 
825713 


4 


55 


174561 


i3 


48 


745306 


3 


14 


919593 


1. 41 


4 


55 


174287 


12 


49 


745494 


3 


14 


919508 


1.41 


825986 


4 


55 


174014 


11 


5o 


745683 


3 


14 


919424 


1. 41 


826259 


4 


55 


173741 


10 


5i 


9-745871 


3 


14 


9.919339 


1. 41 


9-826532 


4 


55 


10.173468 


I 


52 


746059 


3 


14 


919254 


1. 41 


826805 


4 


55 


173195 


53 


746248 


3 


i3 


919169 
• 919085 


1. 41 


827078 


4 


55 


172922 


I 


54 


746436 


4 


i3 


1. 41 


827351 


4 


55 


172649 


55 


746624 


3 


i3 




1. 41 


827624 


4 


55 


172376 


5 


56 


746812 


3 


i3 


Vhll 


1-42 


827897 


4 


54 


172103 


4 


57 


746999 
747187 


3 


i3 


1.42 


828170 


4 


54 


'7'^^S 


3 


58 


3 


12 


918745 


1.42 


828442 


4 


54 


I7i558 


2 


59 


747374 


3 


.12 


918659 


1.42 


828715 


4 


54 


171285 


I 


60 


747562 


3.12 


918574 


1.42 


828987 


4.54 


171013 







Coaine 


D. 


Sine 


D. 


Cotang. 


D. 


Tang. 


mT 



18 



(56 DEGREES.) 



52 



(34 DEGEEES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 







9-747562 


3-12 


9-918574 
918489 


1-42 


9 -828987 


4-54 


10-171013 


60 


I 


747749 


3-12 


1-42 


829260 


4-54 


170740 


u 


2 


748123 


3-12 


918404 


1-42 


829532 


4-54 


170468 


3 


3.U 


9i83i8 


1-42 


829805 


4-54 


,70195 


57 


4 


748310 


3-II 


918233 


1-42 


830077 


4-54 


169923 


56 


5 


748497 


3-II 


918147 


1-42 


83o349 


4-53 


169651 


55 


6 


748683 


3-u 


918062 


1-42 


83o62i 


4-53 


169379 


54 


7 


748870 


3-11 


917976 
917891 


1-43 


830893 


4-53 


,69107 


53 


8 


749056 


3.10 


1-43 


83ii65 


4-53 


168835 


52 


9 


749243 


3-10 


917805 


1-43 


831437 


4-53 


168563 i 5i 


10 


749429 


3-10 


917719 


1-43 


831709 


4-53 


16829, 1 5o 


II 


9-749615 


3.10 


9-917634 


1-43 


9-831981 


4-53 


10-1680,9 4o 


12 


749801 


3-10 


917548 


1.43 


832253 


4-53 


167747 
167475 


48 


i3 


749987 


3-09 


917462 


1.43 


832525 


4-53 


2 


14 


750172 


3-09 


917376 


1.43 


832796 


4-53 


167204 


i5 


75o358 


3.09 


917290 


1-43 


833o68 


4-52 


45 


i6 


75o543 


3.09 


917204 


1.43 


833339 


4-52 


166661 


44 


17 


750729 


3^:^^ 


917118 


1-44 


833611 


4-52 


,66389 
166,18 


43 


i8 


750914 


917032 


1-44 


833882 


4-52 


42 


19 


751284 


3-o8 


916946 
916859 


1-44 


834154 


4-52 


,65846 


41 


20 


3.08 


1-44 


834425 


4-52 


165575 


40 


21 


9-751469 


3-o8 


9-916773 


1-44 


'IS 

835238 


4-52 


io-i653o4 


11 


22 


75i654 


3.08 


916687 


1-44 


4-52 


,65o33 


23 


751839 
752023 


3-o8 


916600 


1-44 


4-52 


,64762 


37 


24 


3.07 


9i65i4 


1-44 


835509 


4-52 


164491 


36 


25 


752208 


3.07 


916427 


1-44 


835780 


4-5i 


164220 


35 


26 


752392 


3.07 


916341 


1-44 


836o5i 


4-5i 


\iin 


34 


27 


732576 
752760 


3.07 


916254 


1-44 


836322 


4-5i 


33 


28 


3.07 


916167 


1-45 


836593 


4-5, 


163407 


32 


29 


752944 


3.06 


916081 


1-45 


836864 


4-5i 


i63i36 


3i 


3o 


753128 


3-o6 


915994 


1-45 


837134 


4-5i 


162866 


3o 


3i 


9-753312 


3-o6 


9-915907 


1-45 


9-8374o5 


4-5i 


10-162595 


li 


32 


753495 


3-o6 


9,5820 


1-45 


837675 


4-5i 


,62325 


33 


753679 


3-06 


915733 


1-45 


837946 


4-5, 


162054 


?6 


34 


753862 


3-05 


915646 


1-45 


838216 


4-5i 


16,784 


35 


734046 


3-o5 


9.5559 


1-45 


838487 


4-5o 


,6,5,3 


25 


36 


754229 


3-05 


915472 


1-45 


838757 


4-5o 


,61243 


24 


37 


754412 


3.o5 


915385 


1-45 


839027 


4-5o 


160973 


23 


38 


754595 


3-o5 


915297 


1-45 


& 


4-5o 


160703 


22 


39 


754778 


3-04 


915210 


1-45 


4-5o 


160432 


21 


40 


754960 


3-04 


9i5i23 


1-46 


839838 


4-5o 


160,62 


20 


41 


9-755x43 


3-04 


9-9i5o35 


1-46 


9-840108 


4-5o 


10-159892 


11 


42 


755326 


3-04 


914948 


1-46 


840378 


4-5o 


159622 


43 


755508 


3-04 


914860 


1-46 


840647 


4-5o 


159353 


17 


44 


7556go 


3-04 


914773 


1.46 


840917 


4-49 


159083 
i588i3 


,6 


45 


755872 


3-03 


914685 


1.46 


841187 


4-49 


,5 


46 


756o54 


3-o3 


914598 


1-46 


841457 
841726 


4-49 


158543 


14 


47 


756236 


3.o3 


914510 


1-46 


4-49 


158274 


i3 


48 


756418 


3 -03 


914422 


1-46 


841996 


4-49 


i58oo4 


12 


49 


756600 


3-03 


914334 


1-46 


842266 


4.49 


157734 


II 


5o 


756782 


3-02 


914246 


1-47 


842535 


4-49 


157465 


10 


5i 


9.756963 


3-02 


9-9141^8 


1-47 


9-842805 


4-49 


10-157,95 


2 


52 


757144 


3-02 


914070 


1-47 


843074 


4-49 


156926 


53 


757326 


3-02 


913982 


1-47 


843343 


4-49 


,56657 


7 


54 


757507 


3-02 


913894 


1-47 


843612 


til 


,56388 


6 


55 


757688 


3-01 


913806 


1-47 


843882 


i56,,8 


5 


56 


]t& 


3-01 


913718 


1-47 


844i5i 


4-48 


,55849 


4 


u 


3-01 


9i363o 


1-47 


844420 


4-48 


,55580 


3 


758230 


3.01 


913541 


1-47 


844689 
844958 


4-48 


j553,i 


2 


59 


7584U 


3-01 


913453 


1-47 


4-48 


,55042 


I 


60 


758591 


3.01 


913365 


1-47 


845227 


4.48 


154773 







Cosine 


D. 


Sine 


D. 


Cotang. 


D. 


Tang. 1 M. | 



(55 DEGREES.) 



StN-ES AXD TANGENTS. (35 DEGREES.) 



53 



M. 


Sine 


D. 


Cosine 1 


>_ 


Tang. 


D. 


Cotiing. j 1 





9.753591 


3-01 


9.913365 1 


47 


845496 
845764 


4-48 


10-154773 


60 


I 


758772 


3-00 


913276 I 


47 


4-48 


I 54504 


is 


2 


758952 


3.00 


913187 I 


48 


4-48 


154236 


3 


759132 


3-00 


913099 I 


48 


846033 


4-48 


I53698 


57 


4 


759312 


3-00 


9i3oio I 


48 


846302 


4-48 


56 


5 


759492 


3-00 


912922 I 


48 


846570 


4-47 


1 53430 


55 


6 


739672 


2-99 


912833 I 


48 


846839 


4.47 


i53i6i 


54 


7 


759852 


2-99 


912744 I 


48 


847107 
847376 


4-47 


152893 


53 


8 


760031 


2-99 


9.2655 I 


48 


4-47 


152624 


52 


9 


7602 I I 


2-99 


912566 I 


48 


847644 


4-47 


152356 


5i 


10 


760390 


2-99 


912477 I 


48 


847913 


4-47 


152087 


5o 


II 


9-760369 


2-98 


9-912388 I 


48 


9.848181 


4-47 


io-i3i8i9 


it 


12 


760748 


2-98 


912299 I 


49 


848449 


4-47 


i5.55i 


i3 


760927 


2-98 


912210 I 


49 


848717 
848986 


4-47 


i5i283 


47 


14 


761 106 


2.98 


912121 I 


49 


4-47 


i5io.4 


46 


i5 


761285 


2-98 


9i2o3i I 


49 


849254 


4-47 


1 50746 


45 


i6 


761464 


2.98 


91 1942 I 


49 


849522 


4-47 


130478 


44 


n 


761642 


2.97 


91.853 I 


49 


849790 


4-46 


i5o2io 


43 


i8 


761821 


2.97 


911763 I 


49 


850038 


4-46 


1^9 


42 


19 


761999 


2-97 


91 1674 I 


49 


85o325 


4-46 


41 


20 


762177 


2.97 


9ii584 I 


49 


800593 


4-46 


149407 


40 


21 


9.762356 


2-97 


9.911495 I 


49 


9-850861 


4-46 


10-149139 


39 


22 


762534 


2.96 


911405 I 


49 


851129 


4.46 


14887 1 


38 


23 


?62889 


2.96 


9ii3i5 I 


5o 


851396 


4-46 


148604 


37 


24 


2.96 


911226 I 


5o 


831664 


4-46 


148336 


36 


23 


763067 


2.96 


9III36 I 


5o 


85i93i 


4-46 


148069 


35 


26 


763245 


2.96 


91 1046 I 


5o 


832199 


4-46 


147801 


34 


27 


763422 


2.96 


910936 I 
910866 I 


5o 


852466 


4-46 


147534 


33 


28 


763600 


2.95 


5o 


852733 


4-45 


147267 


32 


29 


763777 


2.95 


910776 I 


5o 


853001 


4-45 


146999 


3i 


3o 


763934 


2.95 


910686 I 


5o 


853268 


4-45 


146732 


3o 


3i 


9-764131 


2.95 


9.910596 I 


5o 


9.853535 


4-45 


10-146465 


ll 


32 


764308 


2-95 


9io5o6 I 


5o 


853802 


4-45 


146198 


33 


764483 


2-94 


9io4i5 I 


5o 


854069 
854336 


4-45 


145931 


27 


34 


764662 


2-94 


910325 I 


5i 


4-45 


143664 


26 


35 


764838 


2-94 


910235 I 


5i 


854603 


4-45 


145397 
i45i3o 


25 


36 


765oi5 


2-94 


910144 I 


5i 


854870 


4-45 


24 


ll 


765191 


2-94 


910054 I 


5i 


855i37 


4.45 


144863 


23 


765367 


2-94 


909963 I 


5 1 


855404 


4-43 


144596 


22 


39 


765544 


2.93 


909873 I 


5i 


855671 


4-44 


144329 


21 


4o 


765720 


2.93 


909782 I 


5i 


855938 


4-44 


144062 


20 


4i 


9.765896 


2.93 


9.909691 I 


5i 


9-856204 


4-44 


10-143796 


\t 


42 


766072 


2-93 


909601 I 


5i 


856471 


4-44 


143529 
143263 


43 


766247 


2.93 


909510 I 


5i 


856737 


4-44 


17 
16 


44 


'^^Ai'l 


2.93 


909419 I 
909328 I 


5i 


857004 


4.44 


142996 
142730 


45 


766598 


2.92 


52 


857270 


4-44 


i5 


46 


766774 


2.92 


909237 I 


52 


857537 


4-44 


142463 


14 


47 


766949 


2.92 


909146 I 


52 


837803 


4-44 


142 197 


i3 


48 


767124 


2-92 


909055 I 
908964 I 


52 


838060 


4.44 


141931 
I 41 664 


12 


! 49 


767300 


2-92 


52 


858336 


4.44 


II 


i 5o 


767475 


2-91 


908873 I 


52 


858602 


4-43 


141398 


10 


1 '' 


9-767649 


2.91 


9.908781 I 


52 


9-858868 


4-43 


io.i4ii32 


t 


^-' 


767824 


2.91 


908690 I 


52 


839134 


4-43 


140866 


53 


]Ul^ 


2.91 


908599 I 


52 


859400 


4-43 


140600 


7 


^4 


2.91 


908307 I 


52 


859666 


4-43 


i4o334 


6 


1 55 


768348 


2.90 


908416 I 


53 


859932 


4-43 


140068 


5 


56 


768522 


2.90 


908324 I 


53 


860198 


4-43 


139802 


4 


57 


768697 


2.90 


908233 I 


53 


860464 


4.43 


139536 


3 


58 


768871 


2.90 


908141 I 


53 


860730 


4-43 


139270 


2 


59 


769045 


2.90 


» ; 


53 


860995 


4.43 


139005 


I 


60 


769219 


2.90 


53 


861261 


4-43 


i3§739 





1 


Cosine 


D. 


Sine I 


X 


Cotang. 


D. 


Tang. 


^ 



(54 DEGREES.) 



54 



(36 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine 1 I 


). 


Tang. 


D. 


Cotang. 







9-769219 


Ill 


'Z'^&l ; 


.53 


9-861261 


4-43 


10-138739 


60 


I 


769393 


• 53 


861527 


4-43 


138473 


u 


2 


769566 


2.89 


907774 I 


53 


861792 


4-42 


138208 


3 


769740 


2.89 


907682 I 


53 


862058 


4-42 


137942 


u 


4 


769913 


2-89 


907590 I 


53 


862323 


4-42 


137677 


5 


770087 




907498 1 


53 


862389 


4-42 


137411 


55 


6 


770260 


2-88 


907406 I 


53 


862854 


4-42 


137146 
136881 


54 


I 


770433 


2-88 


907314 I 


54 


863 1 19 
863385 


4-42 


53 


770606 


2-88 


907222 I 


54 


4-42 


i366i5 


52 


9 


770779 


2-88 


907129 I 


54 


863650 


4-42 


136350 


5i 


10 


770952 


2-88 


907037 I 


54 


863915 


4-42 


i36o85 


5o 


II 


9.771125 


2-88 


9-906945 I 

906852 I 


54 


9-864180 


4-42 


10-135820 


8 


12 


771298 


2-87 


54 


864445 


4-42 


135555 


i3 


771470 


2-87 


906760 I 
906667 I 


54 


864710 


4-42 


135290 


47 


14 


771643 


2.87 


54 


864975 


4-41 


135025 


46 


i5 


771815 


2.87 


906575 I 


54 


865240 


4-41 


134760 


45 


i6 


771987 


2.87 


906482 I 


54 


8655o5 


4-41 


134495 


44 


\l 


772159 


2.87 


906389 I 


55 


865770 


4-41 


134230 


43 


772331 


2-86 


906296 I 


55 


866035 


4-41 


133965 


42 


19 


772003 


2-86 


906204 1 I 


55 


866300 


4-41 


133700 


41 


20 


772675 


2-86 


906111 I 


55 


866564 


4-41 


133436 


40 


21 


9-772847 
773018 


2-86 


9-906018 I 


55 


9-866829 


4-41 


10-133171 


^1 


22 


2-86 


905025 I 
905832 I 


55 


'£]^l 


4-41 


132906 


23 


773190 


2-86 


55 


4-41 


132642 


37 


24 


773361 


2-85 


905739 I 
905645 I 


55 


867623 


4-41 


132377 


36 


25 


773533 


2-85 


55 


867887 


4-41 


132II3 


35 


26 


773704 


2-85 


905552 I 


55 


868x52 


4-40 


131848 


34 


27 


773875 


2-85 


905459 I 


55 


868416 


4-4o 


I3i584 


33 


28 


774046 


2-85 


905366 I 


56 


868680 


4-40 


i3i32o 


32 


29 


774217 


2-85 


905272 I 


56 


868945 


4-40 


i3io55 


3x 


3o 


774388 


2-84 


905179 I 


56 


869209 


4-40 


130794 


3o 


■ 3i 


9-774558 


2-84 


9-9o5o85 I 


56 


9-869473 


4-40 


io.i3o527 


It 


32 


774729 


2-84 


904992 I 
904898 I 


56 


869737 


4.40 


130263 


33 


774899 


2-84 


56 


870001 


4-40 


\l^ 


11 


34 


775070 


2-84 


904804 I 


56 


870265 


4.40 


35 


775240 


2-84 


9047 1 1 I 


56 


870529 


4-40 


1 2947 1 


25 


36 


775410 


2-83 


904617 I 


56 


870793 
871057 


4-40 


129207 


24 


37 


775580 


2-83 


904523 I 


56 


4.40 


128943 


23 


38 


775750 


2-83 


904429 I 
904335 I 


57 


871321 


4.40 


128679 


22 


39 


775920 


2-83 


57 


871585 


4.40 


1 28415 


21 


40 


776090 


2-83 


904241 I 


57 


871849 


4.39 


I28i5i 


20 


41 


9-776259 


2-83 


9-904147 I 


57 


9-872112 


4-39 


10-127888 


\i 


42 


776429 
77659§ 


2-82 


904053 I 


57 


872376 


4-39 


127624 


43 


2-82 


903959 ' I 
903864 I 


57 


872640 


4-39 


127360 


\i 


44 


776768 


2-82 


57 


872903 


4-39 


127097 


45 


776937 
777106 


2.82 


903770 I 


57 


873167 


4-39 


126833 


i5 


46 


2-82 


903676 1 


57 


873430 


4-39 


126570 


14 


8 


777275 


2-81 


9o358i I 


57 


©^ 


4-39 


i263o6 


x3 


777444 


2-81 


903487 I 


u 


4-39 


1 26043 


X2 


49 


777613 


2-81 


903392 I 


874220 


4-39 


125780 


II 


5o 


777781 


2-81 


903298 I 


58 


874484 


4-39 


1255x6 


10 


5i 


9-777950 


2-81 


9 -903203 I 


58 


9-874747 


4-39 


10-125253 


i 


52 


778119 


2-81 


903 1 08 I 


58 


875010 


4-39 


1 24990 


53 


778287 


2-8o 


9o3oi4 I 


58 


875273 


4-38 


124727 


I 


54 


778455 


2.80 


902919 1 
902824 I 


58 


875536 


4-38 


124464 


55 


778624 


2-8o 


58 


875800 


4-38 


124200 


5 


56 


778792 


2-80 


902729 I 


58 


876063 


4-38 


X 23937 

123674 


4 


u 


778960 


2-80 


902634 I 


58 


876326 


4-38 


3 


779128 


2-80 


902539 I 


59 


876589 


4-38 


1234II 


2 


59 


779295 


2-79 


902444 I 


59 


876851 


4-38 


123x49 


I 


60 


779463 


2-79 


902349 I 


09 


877114 


4-38 


122886 







Cosine 


D. 


Sine 1 E 




Tang. 


D. 


Cotang. 


M. 



(53 DEGREES.) 



SmES AND TANGENTS. (37 DEGREES.) 



55 



M. 


Sine 


D. 


Cosine I 


). 


Taug. 


D. 


Cotaiig. i 





9-779463 


2-79 


9-902349 I 
902253 I 


V 


9-877114 


4-38 


10-122886 


60 


I 


779631 


2 


79 


59 


877377 


4 


38 


122623 


u 


2 


779798 


2 


79 


902158 I 


^9 


877640 


4 


38 


122360 


3 


?32?g 


2 


79 


902063 I 


^9 


l]^ 


4 


38 


122007 


57 


4 


2 


79 


901967 I 
901872 I 


59 


4 


38 


121835 56 


5 


780300 


2 


78 


59 


878428 


4 


38 


121572 i 55 . 


6 


780467 


2 


78 


901776 1 
Q01681 I 


^9 


8789^3 


4 


38 


i2i3o9 54 


7 


780634 


2 


78 


^9 


4 


37 


121047 1 53 


8 


780801 


2 


78 


901585 I 


^9 


879216 


4 


37 


120784 ! 52 


9 


780968 


2 


78 


901490 I 


59 


879478 


4 


37 


120322 


5i 


10 


781134 


2 


78 


901394 I 


60 


879741 


4 


37 


120239 


5o 


u 


9.781301 


2 




9-901298 I 


60 


9 -880003 


4 


37 


10.119997 


S 


12 


781468 


2 




901202 I 


60 


880265 


4 


37 


119735 


i3 


781634 


2 




901 106 I 


60 


880528 


4 


37 


119472 


47 


14 


781800 


2 




901010 I 


60 


880790 
8810D2 


4 


37 


IIQ2I0 1 46 


i5 


781966 


2 




900914 I 
900818 I 


60 


4 


37 


II 8948 


45 


i6 


782132 


2 


?2 


60 


88i3i4 


4 


37 


1 1 8686 


44 


17 


782298 


2 


900722 I 


60 


881576 


4 


37 


118424 


43 


i8 


782464 


2 


76 


900626 I 


60 


881839 




37 


118161 


42 


19 


782630 


2 


76 


900529 I 
900433 I 


60 


882101 


4 


ll 


1 17899 


41 


20 


782796 


2 


76 


61 


882363 


4 


1 1 7637 


40 


21 


9.782961 


2 


76 


9-900337 I 


61 


9.882625 


4 


36 


10.117375 


ll 


22 


783127 


2 


7^ 


900240 I 


61 


882887 


4 


36 


117113 


23 


783458 


2 


75 


900144 I 


6i 


883148 


4 


36 


116852 


37 


24 


2 


75 


900047 I 


6i 


883410 


4 


36 


1 16590 


36 


25 


783623 


2 


75 


is??: ; 


61 


883672 


4 


36 


116328 


35 


26 


783788 


2 


75 


61 


883934 


4 


36 


116066 


34 


11 


783953 


2 


75 


899757 I 


6i 


884196 
884457 


4 


36 


ii58o4 


33 


7841 18 


2 


75 


899660 I 


61 


4 


36 


115543 


32 


29 


784282 


2 


74 


899564 I 


61 


884719 


4 


36 


115281 


3i 


3o 


784447 


2 


74 


899467 I 


62 


884980 


4 


36 


Il5020 


3o 


3i 


9.784612 


2 


74 


9-899370 I 


62 


9-885242 


4 


36 


10-114758 


ll 


32 


784776 


2 


74 


899273 I 


62 


8855o3 


4 


36 


114497 


33 


784941 


2 


74 


899176 I 


62 


885765 


4 


36 


II4235 


ll 


34 


785io5 


2 


74 




62 


8S6026 


4 


36 


113974 


35 


785269 


2 


73 


62 


886288 


4 


36 


113712 


25 


36 


785433 


2 


73 


898884 I 


62 


886549 


4 


35 


ii345i 


24 


ll 


785597 


2 


73 


898787 I 


62 


886810 


4 


35 


113190 


23 


785761 


2 


73 


898689 I 


62 


887072 


4 


35 


112928 
1 1 2667 
112406 


22 


39 


785925 


2 


73 


898592 I 


62 


887333 


4 


35 


21 


40 


786089 


2 


73 


898494 I 


63 


887594 


4 


35 


20 


41 


9-786252 


2 


72 


9-898397 I 


63 


9-887855 


4 


35 


10-112145 


:i 


42 


786416 


2 


72 


898299 I 


63 


8881 16 


4 


35 


111884 


43 


786579 


2 


72 


898202 I 


63 


888377 


4 


35 


111623 


17 


44 


786742 


2 


72 


898104 I 


63 


888639 


4 


35 


iii36i 


16 


45 


786906 


2 


72 


898006 I 


63 


888900 


4 


35 


111 100 


i5 


46 


787069 


2 


72 


897908 I 


63 


889160 


4 


35 


110840 


14 


47 


787232 


2 


71 


897810 I 


63 


889421 


4 


35 


110579 


i3 


48 


1?^?? 


2 


71 


897712 I 


63 


889682 


4 


35 


iio3i8 


12 


49 


2 


71 


897614 I 


63 


889943 


4 


35 


110057 


II 


5o 


787720 


2 


71 


897516 I 


63 


890204 


4 


34 


109796 1 10 1 


5i 


9-787883 


2 


71 


9-897418 I 


64 


9-890465 


4 


34 


10-109535 


I 


52 


788045 


2 


71 


897320 I 


64 


890725 


4 


34 


109273 


53 


788208 


2 


71 


897222 I 


64 


890986 


4 


34 


109014 


1 


54 


788370 


2 


70 


897123 1 I 


64 


891247 


4 


34 


108733 


6 


55 


788532 


2 


70 


897025 i I 


64 


Iglill 


4 


34 


108493 


5 


56 


■7^8694 


2 


70 


806926 1 I 


64 


4 


34 


108232 i 4 


u 


788836 


2 


70 


896828 I 


64 


892028 


4 


34 


107972 3 


789018 


2 


70 


896729 I 


64 


892289 


4 


34 


107711 


2 


59 


789180 


2 


70 


896631 I 


64 


892549 


4 


34 


107431 


I 


60 


789342 


2.69 


896532 I 


64 


892810 


4-34 


107190 







Cosine 


D. 


Sine 1 D. 


Cotang. 


D. 


Tanar. 


IT 



(52 DEGREES.) 



56 



(38 DEGEEES.) A TABLE OF LOGAEITHMIC 



M. 


Sine 


D. 


Cosine I 


). 


Tang. 


D. 


Uotang. 




o 


9.789342 


2 69 


9-896532 I 


64 


9-892810 


4-34 


10-107190 
106930 


60 


1 


789504 


2 


69 


896433 I 


65 


893070 


4-34 


U 


2 


789665 


2 


69 


896335 I 


65 


893331 


4-34 


106669 


3 


789827 


2 


69 


896236 1 


65 


893591 
893851 


4.34 


106409 


u 


4 


789988 


2 


69 


896137 1 


65 


4.34 


106149 


5 


790149 


2 


tl 


896038 I 


65 


8941 1 1 


4-34 


105889 


55 


6 


79o3io 


2 


» ; 


65 


894371 


4-34 


105629 
105368 


54 


7 


790471 


2 


68 


65 


894632 


4-33 


53 


8 


790632 


2 


68 


895741 I 


65 


894892 
895152 


4-33 


io5io8 


52 


9 


790793 


2 


68 


895641 I 


65 


4-33 


104848 


5i 


10 


790954 


2 


68 


895542 I 


65 


895412 


4-33 


104588 


5o 


II 


9-79iii5 


2 


68 


9-895443 I 


66 


9-895672 


4-33 


10.104328 


8 


12 


791275 


2 


67 


895343 I 


66 


895932 


4-33 


104068 


i3 


791436 


2 


67 


895244 I 


66 


896192 
896452 


4-33 


io38o8 


47 


14 


791596 
791757 


2 


67 


895145 I 


66 


4-33 


103548 


46 


ID 


2 


67 


895045 I 


66 


896712 


4-33 


103288 


45 


i6 


791917 


2 


67 


894945 1 
894846 I 


66 


896971 


4-33 


io3o29 


44 


11 


792077 


2 


67 


66 


897231 


4-33 


102769 


43 


792237 


2 


66 


894746 I 


66 


897491 
897751 


4-33 


102509 


42 


19 


792397 


2 


66 


894646 I 


66 


4-33 


102249 


41 


20 


792557 


2 


66 


894546 I 


66 


898010 


4-33 


101990 


40 


21 


9-792716 


2 


66 


9-894446 I 


67 


9.898270 


4-33 


10.101730 


38 


22 


792876 


2 


66 


894346 I 


67 


898530 


4-33 


101470 


23 


793o35 


2 


66 


894246 I 


67 


898789 


4-33 


101211 


37 


24 


793195 
793354 


2 


65 


894146 I 


67 


'& 


4-32 


100951 


36 


25 


2 


65 


894046 I 


67 


4-32 


100602 
100432 


35 


26 


793514 


2 


65 


893946 I 
893846 I 


67 


899568 


4-32 


34 


27 


793673 


2 


65 


67 


899827 


4.32 


100173 


33 


28 


793832 


2 


65 


893745 I 


67 


900086 


4-32 


099914 


32 


29 


793991 


2 


65 


893645 I 


67 


900346 


4-32 


099654 


3i 


3o 


7941 5o 


2 


64 


893544 1 


67 


900605 


4-32 


099395 


3o 


3i 


9 -794308 


2 


64 


9-893444 I 


68 


9 - 900864 


4-32 


io.099i36 

098876 


3 


32 


794467 


2 


64 


893343 I 


68 


901124 


4-32 


33 


794626 


2 


64 


893243 I 


68 


901383 


4.32 


098617 


27 


34 


794784 


2 


64 


893142 I 


68 


901642 


4-32 


098358 


26 


35 


794942 


2 


64 


893041 I 


68 


901901 


4-32 


098099 


2'5 


36 


795101 


2 


64 


892940 I 
892839 I 


68 


902160 


4.32 


097840 


?4 


u 


795259 


2 


63 


68 


902419 


4-32 


097581 


23 


795417 


2 


63 


Zi^ ; 


68 


902679 
902938 


4-32 


097321 


22 


39 


795575 


2 


63 


68 


4-32 


097062 


21 


40 


795733 


2 


63 


892536 1 


68 


903197 


4-31 


096803 


2'0 


41 


9-795891 


2 


63 


9-892435 I 


69 


9-903455 


4-31 


10-096545 


;? 


42 


796049 


2 


63 


892334 I 


69 


903714 


4-3i 


096286 


43 


796206 


2 


63 


892233 I 


69 


903973 


4-3i 


095768 


]i 


44 


796364 


2 


62 


892133 I 


69 


904232 


4-3i 


45 


796531 


2 


62 


892030 I 


69 


904491 
904750 


4-31 


095509 


i5 


46 


796679 


2 


63 


891029 I 
891827 I 


69 


4-3i 


095250 


14 


« 


796836 


2 


62 


69 


9o5oo8 


4-3i 


094992 


i3 


796993 
797 1 5o 


2 


63 


891726 I 


69 


905267 


4-3i 


094733 


12 


49 


2 


61 


891624 I 


69 


905526 


4-3i 


094474 


11 


5o 


797307 


2 


61 


891523 I 


70 


905784 


4-3i 


094216 


10 


5i 


9.797464 


2 


61 


9-891421 I 


70 


9-906043 


4-31 


10.093957 


2 


52 


797621 


2 


61 


891319 1 


70 


9o63o2 


4-3i 


093698 


53 


797777 


2 


61 


891217 1 


70 


9o656o 


4-3i 


093440 


I 


54 


797934 
798091 


2 


61 


891115 I 


70 


9068 1 Q 


4-3i 


093181 


55 


2 


61 


891013 1 


70 


907077 


4-3i 


092923 


5 


56 


798247 


2 


6i 


IX I 


70 


907336 


4-31 


092664 


4 


57 


798403 


2 


60 


70 


907594 
907852 


4.31 


092406 


3 


58 


798560 


2 


60 


890707 1 

8qo6o5 I 


70 


4-3i 


092148 


2 


59 


798716 


2 


60 


70 


908111 


4-3o 


091889 


i 


60 


798872 


2.60 


89o5o3 I 


70 


908369 


4-3o 


091631 







Cosine 


D. 


Sine I 


). 


Cotang. 


D. 


Tang. 1 M. 1 



(51 DEGREES.) 



SINES AND TANGENTS. (39 DEGREJES.) 



57 



M. 


j Sine • 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 







9.79S872 


2-6o 


9-890503 


1-70 


9-908369 
908628 


4-3o 


10-091631 


60 


I 


799028 


2-6o 


890400 


I-7I 


4-3o 


091372 


ll 


2 


799 '84 


2-6o 


890298 


I-7I 


908886 


4-3o 


091114 


3 


799339 


2-59 


890195 


1-71 


909144 


4-3o 


090856 


u 


4 


799493 


2.59 


ii^ 


1-71 


909402 


4-3o 


090398 


5 


7996D1 


2.59 


1-71 


909660 


4-3o 


090340 


55 


6 


799806 


2-59 


1-71 


909918 


4-3o 


090082 


54 


7 


799962 
8001 17 


2-59 


889785 


I-7I 


910177 


4-3o 


089823 


53 


8 


2.59 


889682 


I-7I 


910435 


4-3o 


089365 


52 


9 


800272 


2-58 


889579 


1-71 


910693 
910951 


4-3o 


089307 


5i 


10 


800427 


2-58 


889477 


1-71 


4-3o 


089049 


5o 


M 


9-800582 


2-58 


9-889374 


1-72 


9.9II209 


4-3o 


10-088791 


§ 


12 


800737 


2-58 


889271 


1-72 


911467 


4-3o 


088533 


i3 


800892 


2-58 


889168 


1-72 


911724 


4-3o 


088276 


47 


14 


801047 


2-58 


889064 
888961 


1-72 


911982 


4-3o 


088018 


46 


i5 


801201 


2-58 


1-72 


912240 


4-3o 


087760 


45 


i6 


8oi356 


2.57 


888858 


1-72 


912498 
912756 


4-3o 


087502 


44 


;j 


8oi5ii 


2-57 


888755 


1-72 


4-3o 


087244 


43 


80 1 665 


2.57 


888651 


1-72 


9i3oi4 


4-29 


086986 


42 


19 


801819 


2.5J 


888548 


1-72 


913271 


4-29 


086729 


41 


20 


801973 


2-57 


888444 


1-73 


913529 


4-29 


086471 


40 


21 


9-802128 


2.57 


9-888341 


1.73 


9-913787 


4-29 


io-o862i3 


u 


22 


802282 


2-56 


888237 


1.73 


914044 


4-29 


085936 


23 


802436 


2-56 


888134 


1.73 


914302 


4-29 


083698 


37 


24 


802589 


2-56 


888o3o 


I ••73 


914360 


4-29 


085440 


36 


25 


802743 


2-56 


887926 
887822 


1.73 


914817 


4-29 


o85i83 


35 


26 


802897 


2-56 


1.73 


915075 


4-29 


084925 


34 


27 


8o3o5o 


2-56 


887718 


1.73 


915332 


4-29 


084668 


33 


28 


803204 


2-56 


887614 


1-73 


915590 


4-29 


084410 


32 


^ 


803357 


2-55 


887510 


1-73 


915847 


4-29 


■ 084153 


3i 


So 


8o35ii 


2-55 


887406 


1-74 


916104 


4-29 


083896 


3o 


3i 


9 -803664 


2-55 


9 -887302 


1-74 


9-916362 


4-29 


10-083638 


ll 


32 


803817 


2-55 


887198 


1-74 


916619 


4-29 


o8338i 


33 


803970 


2-55 


887093 


1-74 


916877 


4-29 


o83i23 


27 


¥ 


804123 


2-55 


88690Q 


1-74 


917134 


4-29 


082866 


26 


35 


804276 


2-54 


886885 


1-74 


917391 


4-29 


082609 


25 


36 


804428 


2-54 


886780 


1-74 


917648 


4-29 


082352 


24 


i^ 


804581 


2-54 


886676 


1-74 


917905 


til 


082095 
081837 


23 


804734 


2-54 


886571 


1-74 


918163 


22 


39 


804B86 


2-54 


886466 


1-74 


918420 


4-28 


o8i58o 


21 


4o 


8o5o39 


2-54 


8S6362 


1-75 


918677 


4-28 


o8i323 


20 


4j 


o-8o5f9i 


2-54 


g. 886257 


1.75 


9-918934 


4-28 


10-081066 


:i 


42 


805343 


2-53 


886i52 


1-75 


919191 


4-28 


080809 


43 


805493 


2-53 


886047 


1.75 


919448 


4-28 


o8o552 


\i 


44 


8o5647 


2-53 


885942 


1.75 


919705 


4-28 


080295 


45 


803799 


2-53 


885837 


1-75 


919962 


4-28 


o8oo38 


i5 


46 


805931 


2-53 


885732 


1.75 


920219 


4-28 


079781 


14 


47 


806 I o3 


2-53 


885627 


1-75 


920476 


4-28 


079524 


i3 


48 


806254 


2-53 


885522 


1-75 


920733 


4-28 


079267 


12 


49 


806406 


2-52 


885416 


1-75 


920Q90 


4-28 


079010 


11 


5o 


806557 


2-52 


8853 1 1 


1.76 


921247 


4-28 


078753 


10 


5i 


9-806709 


2-52 


9-885205 


1.76 


9-92i5o3 


4-28 


10-078497 


? 


32 


806860 


2-52 


885100 


1.76 


921760 


4-28 


078240 


53 


80701 1 


2-52 


884^^9 


1.76 


922017 


4-28 


077983 


7 


54 


807163 


2-52 


1.76 


922274 


4-28 


077726 


6 


55 


807314 


2-52 


884783 


1-76 


922530 


4-28 


077470 


5 


56 


807465 


2-5l 


884677 


1.76 


922787 


4-28 


077213 


4 


il 


807615 


2-5l 


884572 


1-76 


923044 


4-28 


076956 


3 


58 


807766 


2-5r 


884466 


1.76 


923300 


4-28 


076700 


2 


59 


807917 


2-5l 


884360 


1-76 


923557 


4-27 


076443 


I 


60 


80S067 


2-51 


884254 


1-77 


9238i3 


4-27 


076187 







Cosine 


D. 


Sine 


D. 


Cotang. 


D. 


Tang. 


"mT 



(50 DEGREES.) 



58 



(40 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 







9.808067 


^.5i 


9.884254 


1-77 


9-9238.3 


4-27 


10.076187 


60 


I 


808218 


2.5l 


884148 


1-77 


924070 


4-27 


075980 


58 


2 


8o8368 


2.5l 


884042 


1.77 


924327 


4-27 


075673 


3 


8o85i9 


2.5o 


883936 
' 883829 


1.77 


924583 


4-27 


075417 


57 


4 


808669 


2.5o 


1.77 


924840 


4-27 


075160 


56 


5 


808819 


2.5o 


883723 
883617 


1.77 


925096 


4-27 


074904 


55 


6 


808969 


2.5o 


1.77 


925352 


4-27 


074648 


54 


I 


8091 19 


2.5o 


883510 


1-77 


925609 
925865 


4-27 


074891 


53 


809269 


2.5o 


883404 


1-77 


4-27 


074135 


52 


9 


809419 


2.49 


883297 


1-78 


926.22 


4-27 


078878 


5i 


10 


809569 


2-49 


883191 


1.78 


926378 


4-27 


078622 


5o 


11 


9.809718 


2-49 


9-883084 


1.78 


9-926634 


4-27 


10.078866 


a 


12 


809868 


2-49 


882977 


1.78 


926890 


4-27 


078110 


i3 


810017 


2-49 


882871 


1.78 


927147 


4-27 


072853 


47 


14 


810167 


2-49 


882764 


1.78 


927403 


4-27 


072597 


46 


i5 


8io3i6 


2.48 


882657 


1.78 


927659 
9279.5 
928171 


4-27 


072841 


45 


i6 


810465 


2.48 


882550 


1-78 


4-27 


072085 


44 


\l 


810614 


2-48 


882443 


1.78 


4-27 


071829 


43 


810763 


2.48' 


882336 


1-79 


928427 


4-27 


071573 


42 


19 


810912 


2.48 


882229 


1-79 


928683 


4-27 


07.3.7 


41 


20 


811061 


2-48 


882l2i 


1-79 


928940 


4-27 


071060 


40 


21 


9.811210 


2.48 


9.8820.4 


1.79 


9.929196 
929452 


4-27 


10.070804 


32 


22 


8ii358 


2-47 


88.907 


1.79 


4-27 


070548 


38 


23 


8ii5o7 


2-47 


881799 


1-79 


929708 


4-27 


070292 
070086 


37 


24 


8ii655 


2-47 


881692 
88.584 


1.79 


929964 


4-26 


36 


25 


81 1804 


2-47 


1-79 


980220 


4-26 


069780 
069525 


35 


26 


811952 


2-47 


88.477 


1-79 


930475 


4-26 


34 


27 


812100 


2-47 


88.369 


1.79 


930731 


4-26 


069269 


33 


28 


812248 


2-47 


88.26. 


1.80 


930987 
931243 


4-26 


32 


29 


812396 


2.46 


88.153 


1.80 


4-26 


3i 


3o 


812544 


2.46 


881046 


1.80 


931499 


4-26 


o685oi 


3o 


3i 


9-812692 


2-46 


9 -880^8 


1.80 


9-931755 


4-26 


10.068245 


29 


32 


812840 


2-46 


1.80 


932010 


4-26 


067990 


28 


33 


812988 


2.46 


880722 


1.80 


932266 


4-26 


067734 


27 


34 


8i3i35 


2-46 


880613 


1-80 


932522 


4-26 


067478 


26 


35 


8i3283 


2-46 


88o5o5 


1.80 


932778 


4-26 


067222 


25 


36 


8i343o 


2.45 


880397 


1.80 


933o33 


4-26 


066967 


24 


37 


813578 


2.45 


880289 


1-81 


933289 


4.26 


0667 1 1 


23 


38 


813725 


2.45 


880180 


1.81 


933545 


4-26 


066455 


22 


39 


813872 


2.45 


880072 


1.81 


933800 


4-26 


066200 


21 


40 


814019 


2-45 


879963 


1. 81 


934o56 


4-26 


065944 


20 


41 


9-814166 


2-45 


9.879855 


1. 81 


9-934311 


4-26 


.0.065689 


;i 


42 


8i43i3 


2-45 


879746 


1. 81 


934567 


4-26 


065433 


43 


814460 


2-44 


879637 


1.8. 


934823 


4-26 


o65i77 


17 


44 


814607 


2-44 


879529 


1. 81 


935078 


4-26 


064922 
064667 


16 


45 


8.4753 


2-44 


879420 


1. 81 


935333 


4-26 


i5 


46 


814900 


2-44 


87931. 


1.8. 


935589 


4-26 


06441 1 


14 


s 


8 1 5046 


2-44 


879202 


1.82 


935844 


4-26 


0641 56 


i3 


815193 


2.44 


8789^4 
878§75 


1.82 


936.00 


4-26 


068900 


12 


49 


815339 
81 5485 


2-44 


1.82 


936355 


4-26 


063645 


J I 


5o 


2-43 


1.82 


936610 


4-26 


068890 


10 


5i 


o-8i563i 


2-43 


9-878766 


1.82 


9-936866 


4-25 


10.068184 


I 


52 


815778 


2-43 


878656 


1.82 


937121 


4-23 


062879 


53 


815924 


2-43 


878547 


1.82 


937376 


4-25 


062624 


1 


54 


816069 
816216 


2-43 


878438 


1.82 


937682 


4-25 


062868 


6 


55 


2.43 


878328 


1.82 


987887 


4-25 


062118 


5 


56 


8i636i 


2-43 


878219 


1.83 


988142 


4-25 


06 1 858 


4 


57 


8i65o7 


2-42 


878109 


1.83 


988898 
938653 


4-25 


061602 


3 


58 1 


8.6652 


2-42 


877999 
877800 
877780 


1.83 


4-25 


061847 


2 


59 I 


816798 


2.42 


1.83 


988908 


4-25 


061092 
060887 


I 


60 [ 


8.6943 


2-42 


1.83 


989168 


4-25 


° 


1 


Cosine 1 


D. 1 


Sine 1 


D. 


Cotang. 


D. 


Tang, i M. | 








(49 


DEGRE 


ES.) 









SINES AND TANGENTS. (41 DEGKEES.) 



59 



M. 


Sine 


D. 


Cosine 


D. 


Tiiug. 


D. 


Cotiing. 







9.816943 


2-42 


9-877780 


1-83 


9-939163 


4-25 


10-060837 


60 


I 


817088 


2-42 


1-83 


939418 


4-20 


o6o582 


u 


2 


817233 


2.42 


1-83 


939673 


4-25 


060327 


3 


817379 


2-42 


877450 


1-83 


939928 


4-25 


060072 


57 


4 


817524 


2.41 


877340 


1-83 


940183 


4-25 


059817 


56 


5 


817668 


2-41 


877230 


1-84 


940438 


4-25 


059562 


55 


6 


817813 


2-41 


877120 


1-84 


940694 


4-25 


059306 


54 


I 


817958 


2-41 


877010 


1-84 


940949 


4-25 


059051 


53 


8i8io3 


2-41 


8767^^ 


1-84 


941204 


4-25 


058796 


52 


9 


818247 


2-41 


1-84 


941458 


4-25 


058542 


5i 


10 


818392 


2-41 


1.84 


941714 


4-25 


058286 


5o 


II 


9-818536 


2.40 


9-876568 


1-84 


9-941968 


4-25 


io.o58o32 


a 


12 


8i868r 


2-40 


876457 


1-84 


942223 


4 25 


057777 
057522 


i3 


818825 


2-40 


876347 


1-84 


942478 


4-25 


47 


i4 


l^ 


2-40 


876236 


1-85 


942733 


4-25 


057267 


46 


i5 


2-40 


876125 


1-85 


942988 


4-25 


057012 


45 


i6 


819257 


2.40 


876014 


1-85 


943243 


4-25 


056757 


44 


'I 


819401 


2.40 


875904 


1-85 


943498 


4-25 


o565o2 


43 


i8 


819045 


2.39 


875793 


1-85 


943702 


4-25 


056248 


42 


19 


819689 


2-39 


875682 


1-85 


944007 


4-25 


055738 


41 


20 


819832 


2-39 


875571 


1-85 


944262 


4-25 


40 


21 


9-819976 


2.39 


9-875459 
875348 


1.85 


9-944517 


4-25 


10-055483 


ll 


22 


820120 


2-39 


1-85 


944771 


4-24 


055229 


23 


820263 


J -39 


875237 


1-85 


945026 


4-24 


054974 


37 


24 


820406 


lit 


875126 


1-86 


945281 


4-24 


05446^ 


36 


25 


82o55o 


875014 


1-86 


945535 


4-24 


35 


26 


820693 


2-38 


874903 


1-86 


945790 


4-24 


054210 


34 


U 


820836 


2-38 


l]X 


1.86 


946045 


4-24 


053955 


33 


820979 


2-38 


1.86 


946299 
946004 


4-24 


053701 


32 


29 


821122 


2-38 


874568 


1.86 


4-24 


053446 


3i 


3o 


821265 


2-38 


874456 


1.86 


946808 


4-24 


053192 


3o 


3i 


9-821407 


2.38 


9-874344 


1.86 


9.947063 


4-24 


10-052937 
052682 


il 


32 


82i55o 


2-38 


874232 


1-87 


947318 


4-24 


33 


821693 


2.37 


874121 


1-87 


947572 


4-24 


052428 


11 


34 


821835 


2.37 


874009 
873896 


1-87 


947826 


4-24 


052174 


35 


821977 


2.37 


1-87 


948081 


4-24 


051919 


25 


36 


822120 


2-37 


873784 


1-87 


948336 


4-24 


o5i664 


24 


U 


822262 


2.37 


'& 


1-87 


948090 


4-24 


o5i4io 


23 


822404 


2-37 


1-87 


948844 


4-24 


o5ii06 


22 


39 


82 2546 


2.37 


873448 


1-87 


949353 


4-24 


050901 


21 


40 


822688 


2-36 


873335 


1.87 


4-24 


050647 


20 


4i 


9.822830 


2-36 


9-873223 


;:S 


9-949607 


4-24 


10 -050393 
o5oi38 


\l 


42 


822972 


2-36 


873110 


949862 


4-24 


43 


823114 


2-36 


&l 


1-88 


950116 


4-24 


049884 


17 


44 


823255 


2-36 


1 .88 


950370 


4-24 


049630 


16 


45 


823397 


2-36 


872772 


1-88 


950625 


4-24 


049375 


i5 


46 


823539 


2.36 


872659 


1-88 


?S?]? 


4-24 


049121 

048867 


14 


8 


823680 


2.35 


872547 


1.88 


4-24 


i3 


823821 


2-35 


872434 


1.88 


95i388 


4-24 


048612 


12 


P 


823963 


2.35 


872321 


1-88 


901642 


4-24 


048358 


11 


5o 


824104 


2-35 


872208 


1.88 


951896 


4-24 


048104 


10 


5i 


9.824245 


2-35 


9-872095 


1.89 


9-952i5o 


4-24 


10-047850 


9 


52 


824386 


2-35 


871081 
871868 


1.89 


952405 


4-24 


047595 


8 


53 


824027 
824668 


2-35 


1.89 


imt 


4-24 


047341 


7 


54 


2-34 


871755 


1-89 


4-24 


047087 
046833 


6 


55 


824808 


2-34 


87 I 641 


1.89 


953167 


4-23 


5 


«^ 


, 824949 


2-34 


871528 


1-89 


953421 


4-23 


046579 


4 


u 


825090 


2-34 


871414 


1-89 


953675 


4-23 


046325 


3 


825230 


2-34 


871301 


1-89 


&I 


4-23 


046071 


2 


^ 


825371 


2-34 


871187 


1.89 


4-23 


045817 


I 


6o 


8255II 


2-34 


871073 


1-90 


954437 


4-23 


045563 





1 


Cosine 


D. 


Sine 


D. 


Cotang. 


D. 


Tang. 


"mT 








(48 


DEGRE 


ES.) 









60 



(42 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine ] 


X 


Tang. 


D. 


Cotaug. 







9-8255II 


2-34 


9-871073 I 


.90 


9-954437 


4.23 


10-045563 


60 


I 


82565: 


2 


33 


870960 I 


90 


954691 


4-23 


045309 
o45o55 


ll 


2 


825791 
825931 


2 


33 


870846 I 


90 


954945 


4-23 


3 


2 


33 


870732 I 


90 


955200 


4-23 


044800 


u 


4 


826071 


2 


33 


870618 I 


90 


955454 


4-23 


044546 


5 


826211 


2 


33 


870504 I 


90 


955707 


4-23 


044298 


55 


6 


826351 


2 


33 


870390 I 


90 


955961 


4-28 


044039 
043785 


54 


7 


826491 


2 


33 


870276 I 


90 


956215 


4-28 


53 


8 


826681 


2 


33 


870161 I 


90 


956469 
956723 


4-28 


o4853i 


52 


9 


826770 


2 


32 


870047 1 


91 


4-28 


043277 


5i 


10 


826910 


2 


32 


869933 I 


91 


956977 


4-23 


048028 


5o 


II 


9-827049 


2 


32 


9-869818 I 


91 


9-957231 


4-23 


10.042769 
o425i5 


49 


12 


827189 


2 


32 


869704 I 


91 


957485 


4-23 


48 


i3 


827328 


2 


32 


869589 1 


91 


957739 


4-23 


042261 


47 


U 


827467 


2 


32 


869474 I 


91 


957993 
958246 


4-23 


042007 


46 


i5 


827606 


2 


32 


869360 I 


91 


4-23 


041754 


45 


i6 


827745 
827884 


2 


32 


869245 I 


91 


958500 


4-28 


o4i5oo 


44 


17 


2 


3i 


869130 I 


91 


958754 


4-28 


041246 


43 


i8 


828023 


2 


3i 


869015 I 


92 


959008 


4-28 


040992 


42 


19 


828162 


2 


3i 


868000 I 


92 


959262 


4-23 


040788 


41 


20 


828301 


2 


3i 


868785 I 


92 


959516 


4-23 


040484 


40 


21 


9-828439 
828578 


2 


3i 


9-868670 I 


92 


9-959769 
960023 


4-28 


10-040281 


39 
38 


22 


2 


3i 


868555 I 


92 


4-23 


089977 


23 


828716 


2 


3i 


868440 I 


92 


960277 


4-23 


089728 


37 


24 


828855 


2 


3o 


868324 I 


92 


960531 


4-28 


089469 
089216 
088962 


36 


25 


828993 


2 


3o 


868209 I 
868093 I 


92 


960784 


4-23 


35 


26 


829131 


2 


3o 


92 


961088 


4-23 


34 


27 


829269 


2 


3o 


^j,t ; 


93 


961 291 


4-28 


088709 
088455 


33 


28 


829407 


2 


3o 


93 


961545 


4-23 


32 


29 


829545 


2 


3o 


867747 I 


93 


961799 
962052 


4-28 


088201 


3i 


3o 


829683 


2 


3o 


867631 I 


93 


4-23 


087948 


3o 


3i 


9-829821 


2 


29 


9-867515 I 


93 


9-962806 


4-28 


10-037694 


11 


32 


829959 


2 


29 


867399 I 
867283 I 


93 


962560 


4-28 


087440 


33 


830097 
830234 


2 


29 


93 


962818 


4-28 


037187 


27 


34 


2 


29 


867167 I 


93 


968067 


4-23 


036988 


26 


35 


83o372 


2 


29 


867051 I 


93 


968820 


4-23 


086680 


25 


36 


83o5o9 


2 


29 


866935 I 
866703 I 


94 


968574 


4-23 


036426 


24 


37 


83o646 


2 


29 


94 


968827 


4-23 


036178 


23 


38 


830784 


2 


li 


94 


964081 


4-23 


08566^ 


22 


39 


830921 


2 


866586 I 


94 


964335 


4-23 


21 


40 


83io58 


2 


28 


866470 I 


94 


964588 


4-22 


035412 


20 


41 


9-831195 


2 


28 


9-866353 i 


94 


9-964842 


4-22 


io.o35i58 


;? 


42 


83i332 


2 


28 


866237 I 


94 


965095 


4-22 


084905 


43 


831469 


2 


28 


866120 I 


94 


965349 


4-22 


03465 1 


\i 


44 


83 1 606 


2 


28 


866004 I 


95 


965602 


4-22 


084898 


45 


831742 


2 


28 


865887 I 


95 


965855 


4-22 


084145 


i5 


46 


831879 
832015 


2 


28 


865770 I 


95 


966105 


4-22 


083891 


14 


s 


2 


27 


865653 I 


95 


966862 


4-22 


033638 


i3 


832152 


2 


27 


865536 I 


95 


966616 


4-22 


033384 


12 


49 


832288 


2 


27 


865419 I 


95 


966869 
967.28 


4-22 


o33i3i 


II 


5o 


832425 


2 


27 


865302 I 


95 


4-22 


082877 


10 


5i 


9-832561 


2 


27 


9-865x85 I 


95 


9-967876 


4-22 


10-082624 


i 


52 


832697 


2 


27 


865o68 I 


95 


967629 


4-22 


082871 


53 


832833 


2 


27 


864950 I 
864833 I 


95 


^'d 


4-22 


082117 


7 


54 


832969 
833 1 o5 


2 


26 


96 


4-22 


081864 


6 


55 


2 


26 


864716 I 


96 


968389 


4-22 


081611 


5 


56 


833241 


2 


26 


864598 1 
864481 I 


96 


968643 


4-22 


081357 


4 


11 


833377 


2 


26 


96 


968896 


4-22 


o3iio4 


3 


833512 


2 


26 


864363 I 


96 


969149 
969403 


4-22 


o8o85i 


2 


59 


833648 


2 


26 


864245 I 


96 


4-22 


o3o597 


I 


60 


833783 


2.26 


864127 I 


96 


969656 


4-22 


080844 







Cosine 


D. 


Sine 1 D. 


Cotang. 


D. 


Tang. 


"mT 



(47 DEGREES." 



SINES AND TANGENTS. (43 DEGREES.) 



61 



M. 


Sine 


D. 


Cosine 


D. 


Tang-. 


D. 


Cotang. 







9.833783 


2-26 


9-864127 


1.96 


9-969656 


4-22 


io-o3o344 


60 


I 


833919 


2 


25 


864010 


1.96 


969909 


4 


22 


o3oo9i 
029838 


ll 


2 


834034 


2 


25 


863892 


1-97 


970162 


4 


22 


3 


834189 


2 


25 


863774 


1.97 


970416 


4 


22 


029584 


57 
56 


4 


834325 


2 


25 


863656 


1.97 


970669 


4 


22 


029331 


5 


834460 


2 


25 


863538 


1.97 


970922 


4 


22 


029078 


55 


6 


834595 
834730 


2 


25 


863419 


1-97 


971175 


4 


22 


028825 


54 


I 


2 


25 


863301 


1.97 


971429 


4 


22 


028571 


53 


834865 


2 


25 


863 1 83 


1-97 


971682 


4 


22 


0283 1 8 


52 


9 


834999 
835i34 


2 


24 


863o64 


1-97 


971935 


4 


22 


028065 


5i 


10 


2 


24 


862946 


1-98 


972188 


4 


22 


027812 


5o 


II 


9.835269 


2 


24 


9-862827 


1.98 


9-972441 


4 


22 


10-027559 


8 


12 


835403 


2 


24 


862709 


1.98 


972694 


4 


22 


027306 


i3 


835538 


2 


24 


862590 


1.98 


972948 


4 


22 


027052 


2 


U 


835672 


2 


24 


862471 


1.98 


973201 


4 


22 


026799 


i5 


835807 


2 


24 


862353 


1.98 


973454 


4 


22 


026546 


45 


i6 


835941 


2 


24 


862234 


1.98 


973707 


4 


22 


026293 


44 


17 


836075 


2 


23 


862115 


1-98 


973960 


4 


22 


026040 


43 


i8 


836209 


2 


23 


861996 


1-98 


974213 


4 


22 


025787 


42 


19 


836343 


2 


23 


861877 


1.98 


974466 


4 


22 


025534 


41 


20 


836477 


2 


23 


861758 


1.99 


974719 


4 


22 


025281 


40 


21 


0.836611 


2 


23 


g.86i638 


1-99 


9.974973 


4 


22 


IO-025027 


ii 


22 


836745 


2 


23 


86i5i9 


1-99 


975226 


4 


22 


024774 


23 


836878 


2 


23 


861400 


1-99 


975479 


4 


22 


024521 


37 


24 


837012 


2 


22 


861280 


1-99 


975732 


4 


22 


024268 


36 


25 


837146 


2 


22 


861161 


1-99 


975985 


4 


22. 


024015 


35 


26 


837279 


2 


22 


86 I 041 


1-99 


976238 


4 


22 


023762 


34 


11 


837412 


2 


22 


860922 
860802 


1-99 


976491 


4 


22 


023509 


33 


837546 


2 


22 


1.99 


976744 


4 


22 


023256 


32 


29 


837679 


2 


22 


860682 


2.00 


976997 
977250 


4 


22 


o23oo3 


3i 


3o 


837812 


2 


22 


86o562 


2-00 


4 


22 


022750 


3o 


3i 


9^^7945 


2 


22 


Q. 860442 


2.00 


9-9775o3 


4 


22 


10-022497 


11 


32 


838078 


2 


21 


86o322 


2-00 


977756 


4 


22 


022244 


33 


8382II 


2 


21 


860202 


2-00 


978009 


4 


22 


021991 


11 


34 


838344 


2 


21 


860082 


2-00 


978262 


4 


22 


021738 


35 


838477 


2 


21 


859^42 


2-00 


9785i5 


4 


22 


021485 


25 


36 


838610 


2 


21 


2-00 


978768 


4 


22 


021232 


24 


3? 
38 


838742 


2 


21 


859721 


2.01 


979021 


4 


22 


020979 


23 


838875 


2 


21 


859601 


2.01 


979274 


4 


22 


020726 


22 


39 


839007 


2 


21 


859480 


2-01 


979527 


4 


22 


020473 


21 


40 


839140 


2 


20 


859360 


2-01 


979780 


4 


22 


020220 


20 


4i 


9-839272 


2 


20 


9.559239 


2.01 


9.980033 


4 


22 


10-019967 


]l 


42 


839404 


2 


20 


859119 
858998 
858877 
858756 


2-01 


980286 


4 


22 


OI9714 


43 


839536 


2 


20 


2-01 


980538 


4 


22 


019462 


17 


44 


839668 


2 


20 


2-01 


980791 


4 


21 


019209 


16 


45 


839800 


2 


20 


2-02 


981044 


4 


21 


018956 


i5 


46 


839932 


2 


20 


858635 


2-02 


981297 
981550 


4 


21 


018703 


14 


47 


840064 


2 


'9 


858514 


2-02 


4 


21 


018450 


i3 


48 


840196 


2 


•9 


858393 


2-02 


981803 


4 


21 


018197 


12 


P 


840328 


2 


19 


858272 


2-02 


982056 


4 


21 


017944 
017691 


II 


5o 


840459 


2 


19 


858i5i 


2-02 


982309 


4 


21 


10 


^' 


9-840591 


2 


19 


9-858029 
857908 


2-02 


9.982562 


4 


21 


10-017438 


I 


52 


840722 
840854 


2 


19 


2-02 


982814 


4 


21 


01 7 1 86 


53 


2 


19 


857786 


2-02 


983067 


4 


21 


016933 


7 


54 


840985 


2 


;§ 


857665 


2-o3 


983320 


4 


21 


016680 


6 


55 


841116 


2 


857543 


2-03 


983573 


4 


21 


016427 


5 


56 


841247 


2 


18 


857422 


2.03 


983826 


4 


21 


016174 


4 


II 


841378 


2 


18 


857300 


2.03 


984079 


4 


21 


015921 


3 


84i5o9 


2 


18 


857178 


2-03 


984331 


4 


21 


015669 


2 


^ 


841640 


2 


18 


857056 


2-o3 


984584 


4 


21 


oi54i6 


I 


6o 


841771 


2-l8 


856934 


2 -03 


984837 


4-21 


oi5i63 







Cosine 


D. 


Sine 


D. 


Cotanar. 


D. 


Tang. 


M. 



(46 



62 



(44 DEGREES.) A TABLE OF LOGARITHMIC 



M. 


Sine 


D. 


Cosine 


D. 


Tang. 


D. 


Cotang. 







9-841771 


2.18 


'■St 


2-03 


9.984837 


4-21 


io-oi5i63 


60 


I 


841902 


2 


-18 


2-o3 


985090 


4-21 


014910 
014657 


u 


2 


842033 


2 




856690 


2-04 


985343 


4-21 


3 


842163 


2 




856568 


2-04 


985596 


4-21 


014404 


57 


4 


842294 


2 




856446 


2-04 


985848 


4-21 


oi4i52 


56 


5 


842424 


2 




856323 


2-04 


986101 


4-21 


013899 


55 


6 


842555 


2 




856201 


2-04 


986354 


4-21 


013646 


54 


I 


842685 


2 




856078 


2.04 


986607 


4-21 


013393 


53 


842815 


2 




855^33 


2-04 


986860 


4-21 


oi3i4o 


52 


9 


842946 


2 




2-04 


9871 12 


4-21 


012888 


5i 


10 


843076 


2 




85571 1 


2-05 


987365 


4-21 


012635 


5o 


II 


9-843206 


2 




9-855588 


2-05 


9-987618 


4-21 


10-012382 


49 


12 


843336 


2 




855465 


2-05 


987871 


4-21 


012129 


48 


i3 


843466 


2 




855342 


2-o5 


988123 


4-21 


011877 


s 


i4 


843595 


2 




855219 


2-05 


988376 


4-21 


011624 


i5 


843725 


2 




855096 


2-o5 


988629 


4-21 


011371 


45 


i6 


843855 


2 




854073 
854850 


2-05 


988882 


4-21 


oiin8 


44 


\l 


843984 


2 




2-05 


989134 


4-21 


010866 


43 


8441 14 


2 




854727 


2-06 


989387 


4-21 


oio6i3 


42 , 


19 


844243 


2 




854603 


2-06 


989640 


4-21 


oio36o 


41 


20 


844372 


2 




854480 


2-06 


989893 


4-21 


010107 


40 


21 


9 -844502 


2 




9-854356 


2-06 


9-990145 


4-21 


10-009855 


S 


22 


844631 


2 




854233 


2-06 


9903^8 


4-21 


009602 


23 


844760 
844889 
84501 8 


2 




854109 


2-06 


4-21 


009349 


37 
36 


24 


2 




853986 


2-06 


990903 


4-21 


008844 


25 


2 




853862 


2-06 


99II56 


4.21 


35 


26 


845147 


2 




853738 


2-o6 


991409 


4-21 


008338 


34 


27 


845276 


2 




853614 


2-07 


991662 


4.21 


33 


28 


845405 


2 




853490 


2-07 


991914 


4-21 


008086 


32 


29 


845533 


2 




853366 


2-07 


992167 


4-21 


007833 


3i 


3o 


845662 


2 




853242 


2-07 


992420 


4-21 


007580 


3o 


3i 


9-845790 


2 




g-853ii8 


2.07 


9-992672 


4-21 


10.007328 


11 


32 


845919 


2 




852Q94 
852869 
852745 


2.07 


992925 


4-21 


007075 


33 


846047 


2 




2.07 


993178 


4-21 


006822 


27 


34 


846175 


2 




2.07 


993430 


4.21 


006570 


26 


35 


846304 


2 




852620 


l:°J> 


993683 


4.21 


oo63i7 


25 


36 


846432 


2 




852496 


993936 


4-21 


006064 


24 


!S 


846560 


2 




852371 


2.08 


994189 


4-21 


oo58ii 


23 


846688 


2 




852247 


2.08 


994441 


4-21 


005559 


22 


39 


846816 


2 




852122 


2-08 


994694 


4-21 


oo53o6 


21 


4o 


846944 


2 




851997 


2-o8 


994947 


4-21 


oo5o53 


20 


4i 


9-847071 


2 




9.851872 


2.08 


9.995199 


4-21 


10-004801 


;i 


42 


847199 


2 




851747 


2.08 


995432 


4-21 


004548 


43 


847327 


2 




85i622 


2.08 


995705 


4-21 


004295 


17 


44 


847454 


2 




85 1 497 


2.09 


995957 


4-21 


004043 


16 


45 


847582 


2 




85i372 


2-09 


996210 


4-21 


003790 


i5 


46 


847709 
847836 


2 




85i246 


2-09 


996463 


4-21 


003537 


14 


S 


2 




85II2I 


2-09 


996715 


4-21 


003285 


i3 


847964 


2 




fX 


2-09 


996968 


4-21 


oo3o32 


12 


49 


848091 


2 




2-09 


997221 


4-21 


002779 
002527 


II 


5o 


848218 


2 




850745 


2-09 


997473 


4-21 


10 


5i 


9-848345 


2 




9.850619 
850493 


2.09 


9.997726 


4-21 


10-002274 


I 


52 


848472 


2 




2-10 


997979 


4-21 


002021 


53 


848599 


2 




85o368 


2-10 




4-21 


001769 
ooi5i6 


I 


54 


848726 


2 




850242 


2-10 


998484 


4-21 


55 


848852 


2 




85oii6 


2-10 


998737 


4-21 


001263 


5 


56 


848979 


2 




849990 


2-10 


998989 


4-21 


OOIOU 


4 


U 


849I06 


2 




849864 


2-10 


999242 


4-21 


060758 


3 


849232 


2 




849738 


2-10 


999495 


4-21 


ooo5o5 


2 


59 


849359 


2 




84961 1 


2-10 


999748 


4-21 


000253 


I 


60 


849480 


2-II 


849485 


2-10 


10.000000 


4-2! 


10-000000 







Cosine 


D. 


Sine 


D. 


Cotan^. 


D. 


Tang. M. | 



(45 DEGREES.) 



A TABLE OF NATUEAL SINES. 



63 



M 




Deg. 


1 Deg. 


2 Deg. 


3 Deg. 


1 4 Deg. 


M 
60 


S. 


C. S. 


S. 


U. S. 
^9-85 


S. 


C. S. 


S. 


C.S. 


S. 


C.S. 


00000 


Unit. 


01745 


03490 


l^lt 


05234 


99863 


06976 


99756 


I 


00029 


I -0000 


01774 
oi8o3 


99984 


o35i9 


o5263 


99861 


07005 


99754 


59 


2 


00058 


I -0000 


99984 


03548 


99937 


05292 


99860 


07034 


99752 


58 


3 


00087 


I -0000 


oi832 


99983 


03577 


99936 


o532i 


99858 


07063 


99750 


57 


4 


00116 


I • 0000 


01862 


99983 


o36o6 


99935 


o535o 


99857 


07092 


99748 


56 


5 


00145 


I -0000 


01891 


99982 


03635 


99934 


05379 
o54o8 


99855 


07121 


99746 


55 


6 


00175 


I -0000 


01920 


99982 


o3664 


99933 


99854 


07i5o 


99744 


54 


7 


00204 


I -0000 


01949 
01978 


99981 


03693 


99932 


05437 


99852 


07179 


99742 


53 


8 


00233 


I-OOOO 


99980 


03723 


99931 


05466 


99851 


07208 


99740 


52 


9 


00262 


I -0000 


02007 


99980 


03752 


99930 


05495 


99849 


07237 


99738 


5i 


10 


00291 


I. 0000 


02036 


99979 


°^78i 


99929 


05524 


99847 


07266 


99736 


5o 


II 


oo32o 


99999 


02c- "^ 


99979 


o38io 


99927 


05553 


99846 


07295 


99734 


^? 


12 


00349 
00378 


99999 


0209^ 


99978 


03839 


99926 


05582 


99844 


07324 


99731 


i3 


99999 


02123 


99977 


03868 


99925 


o56ii 


99842 


07353 


99729 


47 


U 


00407 


99999 


02l52 


99977 


03897 


99924 


o564o 


99841 


07382 


9Q727 


46 


ID 


00436 


99999 


02181 


99976 


03926 


99923 


00669 


99839 


0741 1 


99725 


45 


i6 


00465 


99999 


022II 


99976 


03955 


99922 


05698 


99838 


07440 


99723 


44 


17 


00495 


99999 


02240 


99975 


03984 


99921 


05727 


99836 


07469 


99721 


43 


i8 


oo524 


99999 
99998 


02260 
02298 


99974 


0401 3 


99919 
99918 


05756 


99834 


07498 


99719 
99716 


42 


19 


00553 


99974 


04042 


05785 


99833 


07527 


41 


20 


oo582 


99998 


02327 


99973 


04071 


99917 


o58i4 


99831 


07556 


99714 


40 


21 


006 1 1 


99998 


02356 


99972 


04100 


99916 


o5844 


99829 


07585 


99712 


ll 


22 


00640 


99998 


02385 


99972 


04129 


99915 


05873 


99827 


07614 


99710 


23 


00669 
00698 


99998 


02414 


99971 


04159 


99913 


05902 


99826 


07643 


99708 


37 


24 


99998 


02443 


99970 


04188 


99912 


05931 


99824 


07672 


99705 


36 


25 


00727 


99997 


02472 


99969 


04217 


99911 


05960 


99822 


07701 


99703 


35 


26 


00756 


99997 


025oi 


99969 
99968 


04246 


99910 


05980 


99821 


07730 


99701 


34 


u 


00785 


99997 


o253o 


04275 


99909 


06018 


99819 


07759 
07788 


99699 


33 


00814 


99997 


02560 


99967 


o43o4, 99907 


06047 


99817 


99696 


32 


29 


00844 


99996 


02589 


99966 


04333 


99906 


06076 


99815 


07817 


99694 


3i 


30 


00873 


99996 


02618 


99966 


04362 


99905 


o6io5 


99813 


07846 


99692 


3o 


3i 


00902 


99996 


02647 


99965 


04391 


99904 


06134 


99812 


07875 


99689 


It 


32 


00931 


99996 


02676 


99964 


04420 


99902 


06 1 63 


99810 


07904 


99687 


33 


00960 


99995 


02705 


99963 


04449 
04478 


99901 


06192 


99808 


07933 


99685 


2 


34 


00989 
01018 


99995 


02734 


99963 




06221 


99806 


07962 


99683 


35 


99995 


02763 


99962 


04507 


99098 


o625o 


99804 


07991 


99680 


25 


36 


01047 


99995 


02792 


99961 


04536 


99897 


06279 


99803 


08020 


99678 


24 


37 


01076 


99994 


02821 


99960 


04565 


99896 


o63o8 


99801 


08049 


99676 


23 


38 


oiio5 


99994 


02850 


99959 


04594 


99894 


06337 


99799 


08078 


99673 


22 


39 


oii34 


99994 


02879 
02908 


99959 


04623 


99893 


06366 


99797 


08107 


99671 


21 


40 


J0II64 


99993 


99958 


04653 


99892 


06395 


99795 


o8i36 


99668 


20 


41 


OU93 


99993 


02938 


99957 


04682 


99890 


06424 


99793 


o8i65 


99666 


19 


42 


01222 


99993 


02967 


99956 


047 1 1 


mil 


06453 


99792 


08194 


99664 


18 


43 


0I25l 


99992 


02996 


99955 


04740 


06482 


99790 


08223 


99661 


\l 


44 


01280 99992 1 


o3o25 


99954 


04769 


99886 


o65ii 


99788 


08252 


99659 


45 


oi3o9 


99991 


o3o54 


99953 


04798 


99885 


o654o 


99786 


08281 


99657 


i5 


46 


01338 


99991 


o3o83 


99952 


04827 


99883 


06569 


99784 


o83io 


99654 


14 


47 


01367 


99991 


03lI2 


99952 


04856 


99882 


06598 


99782 


08339 
08368 


99652 


i3 


48 


01396 


99990 


o3i4i 


99951 


04885 


99881 


06627 


99780 


99649 


12 


49 


01425 


99990 


o3i70 


99950 


04914 


99879 
99878 


06656 


99778 


08397 


99647 


II 


5o 


01454 


99989 


o3igQ 


99949 


04943 


06685 


99776 


08426 


99644 


10 


5i 


01483 


99989 


03228 


99948 


04972 


99876 


06714 


99774 


08455 


99642 


9 


52 


oi5i3 


99989 


03257 


99947 


o5ooi 


99875 


06743 


99772 


08484 


99639 


8 


53 


01542' 99988 


03286 


99946 


o5o3o 


99873 


06773 


99770 


o85i3 


99637 


7 


54 


01371 .99988 


o33i6 


99945 


o5o59 
o5o88 


99872 


06802 


99768 


08542 


99635 


6 


55 


01600 999871 


03345 


99944 


99870 


o683i 


99766 


08571 


99632 


5 


56 


01629: 99987^ 


03374 


99943 


o5u7 
o5i46 


?9869 


06860 


99764 


08600 


99630 


4 


11 


01658 


99986 


o34o3 


99942 


99867 


06889 
06918 


99762 


08629 
08658 


99627 


3 


01687 


99986 


03432 


99941 


o5i75 


99866 


99760 


99625 


2 


59 


01716 


99985 


03461 


99940 


o52o5 


99864 


06947 


99758 


08687 


99622 


-4 


"M" 


C.S. 


S. 


C.S. 


S. 


C.S. 


S. 


C.S. 


S. 


C. S. 


S. 


89 Deff. 


88 Deg. 


87 Deg. i 


86 Deg. 1 


85 Deg. 



64 



A TABLE OF NATURAL SINES. 



M 


5 Deg. 


6 Deg. 


1 Deg. 


8 Deg. 


9 Deg. 


M 


S. 


C. S. 


S. 


0. S. 


S. 


C. S. 


S. 


C. S. 


S. 


.0 S. 





08716 


99619 


10453 


99452 


12187 


99255 


18917 


99027 


15643 


98769 


60 


I 


08745 


99617 


10482 


99449 


12216 


99251 


18946 


99028 


15672 


98764 


59 


2 


08774 


99614 


io5ii 


99446 


12245 


99248 


13975 


99019 


15701 


98760 


58 


3 


08803 


99612 


10 540 


99443 


12274 


99244 


14004 


99015 


15780 


98755 


57 


4 


o883i 


99609 


10569 


99440 


12802 


99240 


14033 


990 1 1 


15758 


98751 


56 


5 


08860 


99607 


10597 


99487 


12881 


99287 


14061 


99006 


15787 


98746 


55 


6 


08889 
08918 


99604 


10626 


99434 


12860 


99233 


14090 


99002 


i58i6 


9874. 


54 


7 


99602 


io655 


9943 1 


12889 


99280 


14119 
14148 


98998 


15845 


98787 


53 


8 


08947 


99599 


10684 


99428 


12418 


99226 


98994 


15873 


98782 


52 


9 


08976 


99596 


10713 


99424 


12447 


99222 


14177 


98900 


15902 


98728 


5i 


10 


09005 


99594 


10742 


99421 


12476 


99219 
99215 


14205 


989^6 


1 598 1 


98728 


5o 


II 


09034 


99591 


10771 


99418 


12504 


14284 


^8982 


11$^ 


98718 


49 


12 


09063 


99588 


10800 


99415 


12533 


99211 


14268 


,8978 


98714 


48 


i3 


09092 


99586 


10829 


99412 


12562 


99208 


14292 


98973 


16017 


98709 


47 


14 


ogi2i 


99583 


io858 


99409 


12591 


99204 


14820 


98969 


16046 


98704 


46 


i5 


09i5o 


99580 


10887 


99406 


12620 


99200 


14349 


98965 


16074 


98700 


45 


i6 


09179 


99578 


10916 


99402 


12649 


99197 


14378 


98961 


i6io3 


98695 


44 


',1 


09208 


99575 


10945 


99899 


12678 


99193 
99189 


14407 


98957 


16182 


98600 


43 


09287 


99572 


10973 


99396 


12706 


14436 


98953 


16160 


98686 


42 


19 


09266 


99570 


11002 


99393 


12735 


99186 


14464 


98948 


16189 
16218 


98681 


41 


20 


09295 


99567 


iio3i 


99890 


12764 


99182 


14493 


98944 


98676 


40 


21 


09324 


99564 


'■ 1 1060 


99886 


12798 


99178 


14522 


98940 


16246 


98671 


39 


22 


09353 


99562 


11089 


99888 


12822 


99175 


i455i 


98986 


i62-'5 


98667 


88 


23 


09382 


99559 


iiiiS 


99380 


12851 


99171 


14580 


98931 


16804 


98662 


37 


24 


0941 1 


99556 


1 1 147 


99377 


12880 


99167 


14608 


98927 


16333 


98657 


36 


25 


09440 


99553 


I1I76 


99374 


12908 


99168 


14687 


98923 


1 636 1 


98652 


35 


26 


09469 


99551 


ii2o5 


99370 


12987 


99160 


14666 


98919 


16890 


98648 


34 


27 


0949B 


99548 


11234 


99867 


12966 


99156 


14695 


98914 


16419 


98648 


33 


28 


09D27 


99545 


11263 


99864 


12995 


99152 


14728 


98910 


16447 


98688 


32 


29 


09556 


99542 


11291 


99860 


18024 


99148 


14752 


98906 


16476 


98688 


3i 


3o 


09535 


99540 


Il320 


99357 


i3o53 


99144 


14781 


98902 


i65o5 


98629 


30 


.31 


09614 


99537 


11849 

11878 


99354 


i3o8i 


99141 


14810 


98897 


16533 


98624 


29 
28 


32 


09642 


99534 


99351 


i3iio 


99187 


14838 


98893 


16562 


98619 


33 


09671 


9953. 


1 1407 


99847 


18189 


99188 


14867 


98889 


1659. 


98614 


27 


34 


09700 


99528 


1 1436 


99844 


I3i68 


99129 
99125 


14896 


98884 


16620 


98609 


26 


35 


09720 
09758 


99526 


II465 


99341 


18197 


14925 


98880 


16648 


98604 


25 


36 


99523 


11494 


99337 


18226 


99122 


14904 


98876 


16677 


98600 


24 


37 


09787 


99520 


11523 


99334 


13254 


99.18 


14982 




16706 


98595 


23 


38 


09816 


99517 


ii552 


99331 


18288 


99114 


i5oii 


98867 


16784 


98590 


22 


39 


09845 


99514 


ii58o 


99327 


I33I2 


99110 


1 5040 


98863 


16763 


g8585 


21 


40 


09874 


9951 1 


1 1609 
ii638 


99824 


13841 


99106 


15069 


98858 


16792 


98580 


20 


41 


09903 


99508 


99820 


18870 


99102 


1 5097 


98854 


16820 


98575 


19 
18 


42 


09932 


99506 


1 1667 


99817 


18899 


99098 


i5i26 


98849 


16849 


98570 


43 


09961 


995o3 


1 1696 


99314 


18427 


99094 


i5i55 


98845 


16878 


98565 


17 


44 


09990 


99500 


11725 


99810 


18456 


ITol] 


i5i84 


9^^4' 


16906 


98561 


16 


45 


10019 


99497 


II 754 


99807 


13483 


l5212 


98886 


16985 


98556 


i5 


46 


10048 


99494 


1 1783 


99808 


i35i4 


99088 


i524i 


98882 


16964 


98551 


14 


3 


10077 


99491 


11812 


99800 


13543 


99079 
99075 


15270 


98827 


16992 


98546 


i3 


10106 


99488 


1 1 840 


99297 


18572 


15292 


98828 


17021 


98541 


12 


49 


I0I35 


99485 


U898 


99293 


i36oo 


99071 


15327 


98818 


i7o5o 


98536 


II 


5o 


10164 


99482 


99290 
99286 


18629 


99067 


15356 


98814 


17078 


98581 


10 


5i 


10192 


99479 


11927 


i8658 


99068 


15385 


98809 


17107 
17186 


98526 


9 


52 


10221 


99476 


1 1956 


99283 


13687 


99059 
99055 


15414 


98803 


98521 


8 


53 


I025o 


99473 


1 1985 


99279 


18716 


15442 


98800 


17164 


98516 


7 


54 


10279 


99470 


12014 


99276 


18744 


9905 1 


'^A'^' 


98796 


17198 


98511 


6 


55 


io3o8 


99467 


12043 


99272 


18773 


99047 


i55oo 


98701 
9^787 


17222 


98506 


5 


56 


10337 


99464 


12071 


99269 
99265 


18802 


99043 


'^^^9 


17250 


98501 


4 


ll 


10366 


99461 


12100 


i388i 


99039 
99085 


15557 


98782 


17808 


98496 


3 


10395 


99458 


12129 


99262 


18860 


1 5586 


98778 


98491 


2 


59 


10424 


99455 


12158 


99258 


13889 


9908 1 1 


i56i5 


98773 


17886 


98486 


I 


M 


C. 8. 


S. 


C. S.' 


C. S. S. 


C. S. 


S. 


"cTsT 


S. 


8i Deg. 


83 Deg. 


82 Deg. 


81 Deg. 


80 Deg. 



A TABLE OF NATURAL SINES. 



65 



M 




10 Deg. 


11 Deg. 


12 Deg. 


13 Deg. 


14 Deg. 


60' 


S. 


C. S. 


S. 
1 908 1 


C. S. 


S. 


C.S. 


S. 


C. S. 


S. 


C.S. 


17365 


"98487 


^I63 


20791 


978,5 


^2495 


97437 


24,92 


97o3o 


•i 


17393 


98476 


19109 


98157 


20820 


97809 


22523 


9743o 


24220 


97023 


59' 


2 


17422 


9847. 


19138 


98152 


20848 


97803 


22552 


97424 


24249 


970,5 


58: 


3 


1745. 


98466 


19167 


98146 


20877 


97797 


22580 


97417 


24277 


97008 


^^l 


■4 


17479 


98461 


19195 


98140 


20905 


9779' 


22608 


97411 


243o5 


9700, 


56! 


5 


17508 


98455 


19224 


98135 


20933 


97784 


22637 


97404 


24333 


96994 


551 


6 


17537 


98450 


19252 


98.29 


20962 


97778 


22665 


97398 


24362 


96987 


54 


7 


17565 


98445 


19281 


98124 


20990 


97772 


22693 


97391 


24390 


96980 


53' 


8 


1759/, 


98440 


19309 


98118 


21019 


97766 


22722 


97384 


24418 


96973 


52 i 


9 


17623 


98435 


19338 


98,12 


21047 


97760 


22750 


97378 


24446 


96966 


5i| 


10 


17651 


9S430 


19366 


98107 


21076 


97754 


22778 


97371 


24474 


96959 


5o 


11 


17680 


98425 


19395 


98101 


21104 


97748 


22807 


97365 


245o3 


96952 


49 


12 


17708 


98420 


19423 


98096 


21132 


97742 


22835 


97358 


2453, 


96945 


48 


i3 


17737 


98414 


19452 


98090 


21161 


97735 


22863 


9735, 


24559 


96937 


47 


1 4 


17766 


98409 


19481 


9S084 


21189 


97720 


22892 


97345 


24587 


96930 


46 


i5 


17794 


98404 


19509 


98079 


21218 


97723 


22920 


97338 


246,5 


96923 


45 


i6 


17823 


98399 


19538 


98073 


21246 


97717 


22948 


97331 


24644 


969,6 


44 


17 


17852 


983^i 


19566 


98067 


21275 


9771 1 


22977 


97325 


24672 


96909 


43 


|8 


17880 


98389 


19595 


98061 


2i3o3 


97705 


23oo5 


973i8 


24700 


96902 


42 


19 


17909 


98383 


19623 


98056 


2i33i 


97698 


23o33 


973,1 


24728 


96894 


41 


20 


17937 


98378 


19652 


98050 


2i36o 


97692 


23062 


97304 


24756 


96887 


40 


21 


17966 


983-;3 


19680 


98044 


2i3S8 


97686 


23090 


97298 


24784 


96880 


^ 


22 


17995 


98368 


19709 


98039 


21417 


97680 


23ii8 


97291 


248,3 


96873 


23 


18023 


98362 


19737 


98033 


21445 


97673 


23 146 


97284 


24841 


96866 


ll 


24 


i8o52 


9S337 


19766 


98027 


21474 


97667 


23,75 


97278 


24869 


96858 


25 


18081 


98352 


19794 


98021 


2l502 


9766, 


23203 


97271 


24897 


9685, 


35 


26 


18109 


98347 


19823 


980,6 


2i53o 


97655 


2323, 


97264 


24925 


96S44 


34 


27 


i8i38 


9834. 


19851 


98010 


21559 


97648 


23260 


97257 


24953 


96837 


33 


28 


18166 


98336 


19880 


98004 


21587 


97642 


23288 


97251 


24982 


96829 


32 


29 


18195 


9833. 


19908 


97998 


2,6,6 


97636 


233,6 


97244 


25o,o 


96822 


3i 


30 


18224 


98325 


19937 


97992 


21644 


97630 


23345 


97237 


25o38 


968,5 


3o 


3i 


18252 


98320 


19965 


97987 


21672 


97623 


23373 


97230 


25o66 


96807 


29 


32 


18281 


983 1 5 


19994 


97981 


2,701 


97617 


2340, 


97223 


25094 


96800 


28 


33 


i83o9 


983x0 


20022 


97975 


21729 


97611 


23429 

23458 


97217 


25,22 


96-793 


11 


34 


18338 


983o4 


2005l 


97969 


2,758 


97604 


97210 


25,5, 


96786 


35 


18367 


98299 


20079 
20108 


97963 


2,786 


97598 


23486 


97203 


25,79 


96778 


25 


36 


18395 


98294 


97958 


218,4 


& 


235,4 


97196 
97189 


25207 


96771 


24 


a 


18424 


98288 


2oi36 


97952 


21843 


23542 


25235 


96764 


23 


18452 


98283 


20165 


97946 


2,87, 


97579 


2357, 


97182 


25263 


96756 


22 


39 


18481 


98277 


20193 


97940 


2,899 
21928 


97573 


23599 


97176 


2529, 


96749 


2, 


30 


i85o9 
18538 


98272 


20222 


97934 


97566 


23627 


97,69 


25320 


96742 


20 


41 


98267 


202§0 


97928 


21956 


97560 


23656 


97162 


25348 


96734 


19 


42 


18567 


98261 


20279 


97922 


21985 


97553 


23684 


97155 


25376 


96727 


,8 


43 


18595 


98256 


2o3o7 


979,6 


220,3 


97547 


237,2 


97148 


25404 


96719 


17 


44 


18624 


98250 


20336 


979,0 


22041 


97541 


23740 


97141 


25432 


96712 


,6 


45 


18652 


9824^ 


2o364 


97905 


22070 


97534 


23769 


97134 


25460 


96705 


i5 


46 


18681 


98240 


20393 


97899 


22098 


97528 


23797 


97,27 


25488 


96697 


14 


47 
48 


18710 


98234 


20421 


97893 


22,26 


97321 


23825 


97,20 


255,6 


96682 


i3 


18738 


98220 


2o45o 


97887 


22,55 


975,5 


23853 


97113 


25545 


12 


49 


18767 


98223 


20478 


9788, 


22,83 


97508 


23882 


97,06 


25573 


96675 


II 


5o 


18795 


98218 


2o5o7 


97875 


222,2 


97502 


239,0 


97,00 


256o, 


96667 


10 


5i 


18824 


98212 


2o535 


97869 


22240 


97496 
97489 


23938 


97093 


25629 


96660 


9 


52 


18852 


98207 


20563 


97863 


22268 


23966 


97086 


25657 


96653 


8 


53 


1 888 1 


98201 


20592 


97857 


22297 


97483 


23995 


97079 


25685 


96645 


7 


54 


18910 


98196 


20620} 97851 


22325 


97476 


24023 


97072 


25713 


96638 


6 


55 


18938 


98190 


20649I 97845 


22353 


97470 


24o5i 


97065 


25741 


96630 


5 


56 


18967 


98185 


20677 


97839 


22382 


97463 


24079 


97058 


25769 


96623 


4 


57 


18995 


98,79 


20706 


97833 


22410 


97457 


24108 


97o5i 


25798 


966,5 


3 


58 


19024 


98174 


20734 


97827 


22438 


97450 


24136 


97044 


25826 96608 


2 


59 


19052 

C. S. 


98168 
1 S. 


20763 


97821 


22467 


97444 


24164 


97037 


25854, 96600 

c. s. I s. 


Zj 


C. S. 


S. 


c.s. 


S. 


C.S. 


S. 


79 Deg. 


78 Deg. 


1 77 Deg. 


76 Deg. 


"75 ] 


Deg. 



A TABLE OF NATUEAL SINES. 



M 




15 Beg. 


16 Beg. 


11 Beg. 


1 18 Deg. 


19 Deg. 


M 


S. iC.S. 
25882 96593 
25910 96585 


S. 


C. S. 


S. 1 c. s. 


r s. 


C. S. 


S. 1 s.c. 


27564 


96126 


29237 9563o'! 30902 


95106 


32557 94552 


"60 


I 


27592 


96118 


29265 95622 


j 30929 


95097 


32584' 94542 


'59 


2 


25938 


96578 


27620 


96110 


29293 956i3 


30985 


95088 


3261 2^ 94533 


58 


3 


25966 


96570 


27648 


96102 


29321 


o56o5 


95079 


32639' 94523 


57 


4 


25994 


1 96562 


27676 


96094 


29348 


95506 


31012 


95070 


32667 94514 


56 


5 


26022 


96555 


27704 


96086 


29376 


95588 


31040 


95061 


32694 94504 


55 


6 


26o5o 


1 96547 


27731 


96078 


29404 


95579 


31068 


95o52 


32722 


94495 


54 


I 


26079 


' 96540 


27759 


96070 


29432 


95571 


31095 


95043 


32749 


94485 


53 


26107 


96532 


27787 


96062 


29460 


95562 


31123 


95o33 


32777 


94476 


52 


9. 


26i35 


96524 


27815 


96054 


29487 


95554 


3n5i 


95024 


32804 


94466 


5i 


10 


26163 


' 96517 


27843 


96046 


2951 5 


95545 


! 31178 


95oi5 


32832 


94457 


5o 


II 


26191 


96509 


27871 


96037 


29543 


95536 


3 1 206 


95006 


3 2859 1 04447 


49 


12 


26219 


96502 


27899 


96029 


29571 


95528 


3x233 


94997 


32887 94438 


48 


i3 


- 26247 


96494 


27927 


96021 


29599 
29626 


95519 


31261 


94988 


32914 


94428 


47 


14 


26275 


96486 


27955 


96013 


95511 


31289 


94979 


32942 


94418 


46 


1 5 


263o3 


96479 


27983 


96005 


29654 


95502 


3i3i6 


94970 


32969 


94409 


45 


i6 


2633 1 


96471 


28011 


95997 


29682 


95493 
95485 


3 1344 


94961 


32997 


94399 


44 


17 


26359 


96463 


28039 


95989 


29710 


31372 


94952 


33024 


94390 


43 


i8 


26387 


96456 


28067 


95981 


29737 


95476 


3i399 


94943 


33o5i 


94380 


42 


19 


26415 


96448 


28095 


95972 


29765 


95467 


31427 


94933 


33079 


94370 


41 


20 


26443 


96440 


28123 


95964 


29793 


95459 


3 1 454 


94924 


33 1 06 


94361 


40 


21 


26471 


96433 


28i5o 


95956 


29821 


95450 


31482 


94915 


33 1 34 


94351 


3^ 


22 


26500 


96425 


28178 


95948 


29849 


95441 


3i5io 


94906 


33i6i 


94342 


23 


26528 


96417 


28206 


95940 


29876 


95433 


3i537 


l'& 


33189 


94332 


37 


24 


26556 


96410 


28234 


95931 


29904 


95424 


3i565 


33216 


94322 


36 


25 


26584 


96402 


28262 


95923 


29932 


95415 


31593 


94S78 


33244 


9431 3 


35 


26 


26612 


96394 


28290 


95915 


29960 


95407 


31620 


94869 


33271 


94303 


34 


27 


26640 


96386 


283 18 


95907 


29987 


95398 
95389 


31648 


94860 


33298 


94293 


33 


28 


26668 


96379 


28346 


95898 


3001 5 


31675 


94851 


33326 


94284 


32 


29 


26696 


9637. 


28374 


95890 


30043 


95380 


31703 


94842 


33353 


94274 


3i 


3o 


26724 


96353 


28402 


95882 


30071 


95372 


31730 


94832 


33381 


94264 


3o 


3i 


26752 


96355 


28429 


95874 


30098 


95363 


3i758 


94823 


33408 


94254 


29 


32 


26780 


96347 


28457 


95865 


30126 


95354 


31786 


94814 


33436 


94245 


28 


33 


26S08 


96340 


28485 


95857 


30154 


95345 


3i8i3 


94805 


33463 


94235 


11 


34 


26836 


96332 


285i3 


95849 


30182 


95337 


31841 


94795 


33490 


94225 


35 


26864 


96324 


28541 


95841 


30209 


95328 


3 1 868 


94786 


33518 


94215 


25 


36 


26892 


96316 


28569 


95832 


30237 


95319 


31896 


94777 


33545 


94206 


24 


37 


26920 


9630.8 


28597 


95824 


30265 


95310 


31923 


94768 


33573 


94196 


23 


38 


26948 


96301 


28625 


95816 


30292 


95301 


3i95i 


94758 


33600 


94186 


22 


39 


26976 


96293 


28652 


95807 


3o32o 


95293 


31979 


94749 


336?I 


94176 


21 


40 


27004 


96285 


28680 


95799 


30348 


95284 


32006 


94740 


33655 


94167 


20 


41 


27032 


96277 


28708 


95791 


30376 


95275 


32034 


94730 


33682 


94157 


19 
18 


42 


27060 


96269 


28736 


95782 


3o4o3 


95266 


32061 


94721 


33710 


94147 


43 


27088 


96261 


28764 


95774 


3043 1 


95257 


32089 


94712 


33737 


94137 


17 


44 


27116 


96253 


28792 


95766 


3o45q 


95248 


32116 


94702 


33764 


94127 


16 


45 


27144 


96246 


28820 


95757 


30486 


95240 


32144 


94693 


33792 


94118 


i5 


46 


27172 


96238 


28847 


95749 


3o5i4 


90231 


3217. 


946S4 


33819 


94108 


14 


47 


27200 


96230 


28875 


95740 


30542 


95222 


32199 


94674 


33846 94098 
33874 94088 


i3 


48 


27228 


96222 


28903 


95732 


30570 


95213 


32227 


94665 


12 


49 


27256 


96214 


28931 


95724 


30597 


95204 


32254 


94656 


33901 94078 


II 


5o 


27284 


96206 


28959 


95715 


30625 


95195 


32282 


94646 


33929 94068 


10 


5i 


27312 


96198 


28987 


95707 


3o653 


95 1 §6 


32309 


94637 


33956J 94o58 


9 


52 


27340 


96190 


29015 


95698 


30680 


95177 


32337 


94627 


339831 94049 


8 


53 


27368 


96182 


29042 


95690 


30708 


95168 


32364 


94618 


34011! 94039 


7 


54 


27396 


96174 


29070 


95681 


30736 


95159 


32392 


94609 


34038 


94029 


6 


55 


27424 


96166 


29098 


95673 


30763 


95i5o 


32419 


94599 


34065 


94019 


5 


56 


27452 


96158 


29126 


95664 


30791 


95142 


32447 


t&To 


34093 


94009 


4 


57 


27480 


96150 


29154 


95656 


30819 


95i33 


32474 


34120 


&l 


3 


58 


27508 


961421 


29182 


95647 


30846 


95124 


32502 


94571 


34147 


2 


59 
M 


27536 


96134 


29209 
C. S. 


95639 

S. 


30874 
C. S. 


95ii5 

S. 


32529 


94561 


34175s 93979 
C. S. 1 s. 


1 


C. S. 


S. 


74Deff. 1 


7BBeg. 1 


72 Beg. 


nBeg. 1 


70 Deg. 



A TABLE OF NATURAL SINES. 



r 


i 20 Deg. 


21 Beg. 


22 Deg. 


23 Deg. 


24 Deg. 


M 


M 


i iS. 


C.S. 


S. 


C.S. 


S. 


C.S. 
92718 


S. 
39073 


C.S. 
92o5o 


S. 
-4-^74 


C.S. 





34202 


93969 


l^f-^ 


93358 


?^4^i 


9,355| 60 i 


I 


34229 


93959 


35864 


93348 


37488 


92707 


39,00 


92039M 40700 


9,343 


§1 


2 


34207 


93949 


35891 


93337 


37015 


92697 


39.27 


92028 1 40727 


9,33i 


3 


34284 


93939 


359,8 


93327 


37342 


92686 


39,53 


920, 6| 40753 


9,3,9 


57: 


4 


343x1 


93929 


30945 


93316 


37069 


92675 


39,80 


92005 j 40780 


9,307 


56: 


5 


34339 


93919 


30973 


93306 


37090 


92664:; 39207 


9,994; 40806 


91295 


55] 


6 


34366 


93909 


36000 


93295 


37022 


92653 


39234 


91982 


40833 


9,283 


54! 


I 


34393 


93899 


36027 


93285 


37649 


92642 


! 39260 


9,971 


40860 


9,272 


53 1 


34421 


93889 


36o54 


93274 


37676 


92631 


39287 


9,959 


40886 


9,260 


52; 


9 


34448 


93879 


36081 


93264 


37703 


92620 


393,4 


91948 


409,3 


9,248 


5i 


10 


34475 


93S69 


36108 


93253 


37730 


92609 


39341 


91936' 4og3q 


9,236 


5o 


II 


345o3 


^3859 


36i35 


93243 


37757 


92598 


39367 
39394 


91925 


40966 


9,224 


s 


12 


34530 


93849 


36162 


93232 


37784 
37811 


9^^^I 


9,914 


40992 


9,2,2 


i3 


34557 


93839 


36190 


g3222 


92576 


39421 


91002 
9,89, 


410,9 


9,200 


47 


i4 


34584 


93829 


36217 


93211 


37838 


92565 


39448 


4,045 


91,88 


46: 


i5 


34612 


93819 


36244 


93201 


37865 


92554 


39474 


91879 


41072 


9, ,76 


45 


i6 


34639 


93809 


36271 


93190 

93180 


37892 


92543 


3950, 


9,868 


41098 


91,64 


44 


17 


34666 


93799 


36298 


37919 


92532 


39528 


9,856 


41,25 


9, ,52 


43 


34694 


93789 


36325 


93169 


37946 


92521 


39555 


9,845 


4ii5, 


9,, 40 


42 


19 


34721 


93779 


36352 


93 1 59 

93148 


37973 


925,0 


3958f 


9,833 


41178 


9, ,28 


41 


20 


34748 


93769 


36379 


37999 


92499 


39608 


91822 


41204 


9, ,,6 


40 


21 


34775 


93759 


36406 


93i37 


38026 


92488 


39635 


9,810 


4123, 


9,, 04 


^ 


22 


34803 


93748 


36434 


93127 


38o53 


92477 


3966, 


9 '799 


41257 


9,092 
91080 


23 


34830 


93738 


36461 


93n6 


38o8o 


92466 


39688 


917S7 


4,284 


S 


24 


34857 


93728 


36488 


93106 


f.'V 


92455 


397,5 


9,775 


4,3io 


9,068 


20 


34884 


93718 


365i5 


93095 


38i34 


92444 


3974, 


91764 


4,337 


9,o56 


35 


26 


34912 


93708 


36542 


93084 


38i6i 


92432 


39768 


9,752 


4,363 


91044 


34 


27 


34939 


93688 


36569 


93074 


38i88 


92421 


39795 


9,741 


4,390 


9,032 


33 


28 


34966 


36596 


93o63 


382i5 


92410 


3q82 2 


91729 
91718 


41416 


9,020 


32 


29 


34993 


93677 


36623 


93o52 


38241 


92399 


39848 


41443 


91008 


3i 


30 


35021 


93667 


36650 


93042 


38268 


92388 


39875 


91706 


4,469 


90996 


3o 


3i 


35048 


93657 


36677 


93o3i 


3S295 


92377 


39902 


l\lli 


4,496 


90984 


29 


32 


35075 


93647 


36704 


93020 


38322 


92366 


39928 


4,522 


90972 


28 


33 


35io2 


93637 


36731 


93010 


f^.^i 


92355 


39955 


91671 


4,549 


90960 


27: 


34 


35i3o 


93626 


36758 


92999 


38376 


92343 


39982 


91660 


4,575 


90948 


26; 


35 


35i57 


936i6 


36785 


92988 


38403 


92332 


40008 


91648 


4,602 


90936 


25 


36 


35i83 


93606 


36812 


92978 


38430 


92321 


4oo35 


9,636 


41628 


90924 


24 


S 


352II 


93596 


36839 


92967 


38456 


92310 


40062 


9,625 


4,655 


909,1 


23 


12^ 


93585 


36867 


92956 


38483 


92299 


400S8 


916,3 


4168, 


a 


22 


39 


93575 


36894 


92945 


38510 


92287 


4o,i5 


9,60, 


41707 


21 


40 


35293 


93565 


36921 


92935 


38537 


92276 


40141 


9,590 


4,734 


90875 


20 


41 


35320 


93555 


36948 


92924 


38564 


92265 


40168 


9,578 


4,760 


90863 


% 


^l 


35347 


93544 


36975 


92913 


\lV' 


92254 


40195 


9,566 


41787 


9o85i 


43 


35375 


93534 


37002 


92902 
92892 


38617 


92243 


4022, 


9,555 


418,3 


90839 


17 


44 


35402 


93524 


37029 


38644 


9223, 


40248 


9,543 


41840 


90826 


16 


45 


35429 


93514 


37056 




38671 


92220 


40275 


9,531 


41866 


90814 


i5 


46 


35456 


935o3 


37083 


92870 


38698 


92209 


4o3o, 


& 


41892 


90802 


14 


47 


35484 


93493 


37110 


92859 


3^7?5 


92IQ8 


40828 


41919 


90790 


i3 


48 


355II 


93483 


37137 


92849 


^I'^^l 


92186 


40355 


91496 
9,484 


41945 


90778 


12 


49 


35538 


93472 


37164 


Q2838 


f.V^- 


92175 


4o38, 


41972 


90766 


11 


5o 


35565 


93462 


37191 


92827 


38800 


92164 


40408 


91472 


41998 


90753 


10 


5i 


35592 


93452 


37218 


92816 


38832 


92,52 


40434 


9,461 


42024 


90741 


I 


52 


35619 


93441 


37245 


92805 


38859 


92,4, 


4046, 


9,449 


42o5i 


90729 


53 


35647 


93431 


37272 


92794 


38886 


92i3o 


40488 


91437 


42077 


907,7 


1 


54 


35674 


93420 


37299 


92784 


389,2 


92, ,9 


4o5i4 


9,425 


42,04 


90704 


6 


55 


35701 


93410 


37326 


92773 


38939 


92,07 


4004, 


91414 


42, 3o 


?a 


5 


56 


35728 


93400 


37353 


92762 


38966 


t% 


40567 


91402 


42,56 


4 


57 


35755 


93389 


37380 


92751 


38993 


40094 


9,390 


42,83 


90668 


3 


58 


35782 


& 


37407 


92740 


39020 


92073 


4062, 


9,378 


42209 


90655 


2\ 


59 
M 


358io 


37434 
C.S. 


92729 
S. 


39046 
C.S. 


92062 
S. 


40647 


9,366 


_42235 


90643 




C.S. 


S. 


C.S. 


S. 


C.S. 


s. 


69 Deg. 


68 Deg. 


67 Deg. 1 


66 Deg. 1 


65 Deg. 1 



19 



A TABLE OF NATURAL SINES. 



M 


25 Deg. 


26 Deg. 


27 Deg. 


28 Deg. 


29 


Deg. 


M 


S. 


C. S. 


S. 


c. s. 


S. 


C. S. 


S. 


C. S. 


^s'^ 


C. S. 





42262 


9063 1 


43837 


89879 
89867 


S? 


89101 


46947 


88295 


48481 


87462 


60 


I 


42288 


90618 


43863 


89087 


46973 


88281 


485o6 


87448 


58 


2 


423i5 


90606 


4388g 
439.6 


89854 


4545x 


89074 


46999 


88267 


48532 


87434 


3 


42341 


90594 


8984X 


45477 


89061 


47024 


88254 


48557 


87420 


57 


4 


42367 


90582 


43942 


89828 


455o3 


89048 


47o5o 


88240 


48583 


87406 


56 


5 


42394 


90569 


43968 


89816 


45529 


89035 


47076 


88226 


48608 


8739X 


55 


6 


42420 


90557 


43994 


89803 


45554 


89021 


47101 


88213 


48634 


87377 


54 


7 


42446 


90545 


44020 


89790 


45580 


89008 


47127 


88199 


48659 


87363 


53 


8 


42473 


90532 


44046 


89777 


45606 


S??5 


47153 


88i85 


48684 


87349 
87335 


52 


9 


42499 


90520 


44072 


89764 


45632 


47178 


88x72 


48710 


5i 


10 


42525 


90507 


44098 


89752 


45658 


88968 


47204 


88x58 


48735 


8732X 


5o 


II 


42552 


90495 


44124 


89739 


45684 


88955 


47229 


88144 


48761 


87306 


49 


12 


42578 


90483 


441 5x 


89726 


45710 


88942 


47255 


88i3o 


48786 


87292 


48 


i3 


42604 


90470 


44177 


89713 


45736 


88928 


47281 


88117 


4881 1 


87278 


47 


14 


4263 1 


90458 


44203 


89700 


45762 


88915 


47306 


88io3 


48837 


87264 


46 


i5 


42657 


90446 


44229 


89687 


45787 


88902 


47332 


88089 


48862 


87250 


45 


i6 


42683 


90433 


44255 


89674 


458? 


88888 


47358 


88075 


48888 


87235 


44 


\l 


42709 


90421 


4428X 


89662 


45865 


88875 


47383 


88062 


48913 


87221 


43 


42736 


90408 


44307 


89649 


88862 


47409 


88048 


48938 


87207 


42 


19 


42762 


i:lt 


44333 


89636 


45891 


88848 


47434 


88034 


48964 


87193 


41 


20 


42788 
42815 


44359 


89623 


459x7 


88835 


47460 


88020 


48989 


87178 


40 


21 


90371 


44385 


89610 


45942 


88822 


47486 


88006 


49014 


87164! 39! 


22 


42841 


90358 


44411 


89597 


45968 


88808 


47511 


87993 


49040 


87i5o 


38 


23 


42867 


90346 


44437 


89584 


45994 


88705 


47537 


87979 


49065 


87136 


37 


24 


42894 


90334 


44464 


8957, 


46020 


88782 


47562 


87963 


49090 


87121 


36 


25 


42920 


90321 


44490 


89558 


46046 


88768 


47588 


87951 


49116 


87107 


35 


26 


42946 


90309 


445x6 


89545 


46072 


88755 


47614 


87937 


49141 


87093 


34 


11 


42972 


90296 
90284 


44542 


89532 


46097 


88741 


47639 
47665 


87923 


49166 


87079 


33 


gs 


44568 


895,9 


46x23 


88728 


87909 


49192 


87064 


32 


29 


90271 


44594 


89506 


46149 


88715 


47690 


87896 
87882 


49217 


87o5o 


3i 


3o 


43o5i 


90259 


44620 


89493 


46x75 


88701 


47716 


49242 


87036 


3o 


3i 


43077 


90246 


44646 


89480 


46201 


88688 


47741 


87868 


49268 


87021 


29 


32 


43x04 


90233 


44672 


89467 


46226 


88674 


47767 


87854 


49293 


87007 


28 


33 


43i3o 


90221 


44698 


89454 


46252 


88661 


47793 


87840 


49318 


86993 


27 


34 


43 1 56 


90208 


44724 


89441 


46278 


88647 


47818 


87826 


49344 


86978 


26 


35 


43182 


90196 


44750 


89428 


46304 


88634 


47844 


87812 


49369 


86964 


25 


36 


43209 


90183 


44776 


89415 


46330 


88620 


47869 
47895 


87798 
87784 


49394 


86949 


24 


37 


43235 


90171 


44802 89402 


46355 


88607 


4941? 
49445 


86935 


23 


38 


43261 


90x58 


44828 89389 


46381 


88593 


47920 


87770 


86921 


22 


39 


43287 


90146 


44854 89376 


46407 


88580 


47946 


87756 


49470 


86906 


21 


40 


433 1 3 


90133 


44880 89363 


46433 


88566 


47971 


87743 


49495 


86892 


20 


41 


43340 


90120 


449061 89350 


46458 


88553 


47997 


87729 
87715 


49521 


86878 


19 


42 


43366 


90108 


44932! 89337 


46484 


88539 
88526 


48022 


49546 


86863 


18 


43 


43392 


90095 


44958! 89324 


46510 


48048 


87701 


49571 


86849 


17 


44 


43418 


90082 


44984I 8931. 


46536 


885 1 2 


48073 


87687 


49596 


86834 


16 


45 


43445 


90070 


45oio 89298 


46561 


88499 


48099 


87673 


49622 


86820 


i5 


46 


43471 


90057 


45o36 


89285 


46587 


88485 


48124 


87659 


49647 


868o5 


14 


47 


43497 


90045 


45062 


89272 


46613 


88472 


481 5o 87645 


49672 


86791 


i3 


48 


43523 


90032 


45o88 


89259 
89245 


46639 


88458 


48175 87631 


49697 


86777 


12 


49 


43549 
43575 


90019 


45ii4 


46664 


88445 


48201 87617 


49723 


86762 


II 


5o 


90007 


45 1 40 


89232 


46690 


88431 


48226: 87603 


49748 


86748 


10 


5i 


43602 


89994 


45x66 


892x9 


46716 


88417 


48252 87589 
48277I 87575 


49773 


86733 


9 


52 


43628 


89981 


451921 89206! 


46742 


88404 


49798 


86719 


8 


53 


43654 


89968 


452x8 


89193 

89x^0 


46767 


88390 


483o3 


87561 


49824 


86704 


7 


54 


43680 


89956 


45243 


46793 
46819 


88377 


48328 


87546 


49849 


86690 


6 


55 


43706 


89943 


45269 
45295 


89167 


88363 


48354 


87532 


49874 


86675 


5 


56 


43733 


89930 


89x53 


46844 


88349 


48379 


87518 


49899 


86661 


4 


57 


43759 
43785 


89918 


453 2 X 


89140 


46870 


88336 


48405 


87504 


49924 


86646 


3 


58 


89005 


45347 


89127 


46896: 88322 


48430 


87490 


49950 


86632 


2 


59 


438 1 1 


89§92 


45373 


89x14 


46921 883o8 


48456 


87476 


49975 


86617 


I 
-M 


C. S. 


S. 


c. s. 1 s. 


C. S. 


S. 


C. S. 


S. 


C. S.' 


S. 


64 Deff. 1 


63 Deg. 


62 Deg. 1 


61 Deg. 1 


60 Deg. 1 





A TABLE OF NATURAL SINES. 



69 



M 




30 Beg. 


31 Beg. 


32 Deg. 


83 Deg. 


34 Beg. 


M 
60 


S. 


C.S. 


S. 
5x504 


C.S. 

857.7 


S. 


C.S. 


S. 


C. S. 


S. 


C.S. 


5oooo 


866o3 


52992 


84805 


54464 


83867 


55919 


82904 


I 


50025 


86588 


5x529 


85702 


53017 


84789 


54488 


8385. 


55943 


82887 


U 


2 


5oo5o 


86573 
86559 


5x554 


85687 


53o4. 


84774 


545.3 


83835 


55968 


82871 


3 


50076 


5x579 


85672 


53066 


84759 


54537 


838,9 


55992 


82855 


57 


4 


5oioi 


86544 


5 1 604 


85657 


5309. 


84743 


5456. 


838o4 


56oi6 


82839 


56 


5 


50126 


86530 


5x628 


85642 


53.15 


84728 


54586 


83788 


56040 


82S22 


55 


6 


5oi5i 


865x5 


5x653 


85627 


53.40 


84712 


54610 


83772 


56o64 


82806 


54 


3 


50176 


86501 


51678 


856.2 


53.64 


84697 


54635 


83756 


56o88 


82790 


53 


5020I 


86486 


51703 


85597 


53.89 


8468 X 


54659 


83740 


56. .2 


82773 


52 


9 


50227 


86471 


5x728 


85582 


53214 


84666 


54683 


83724 


56.36 


82757 


5r 


10 


50252 


86457 


5.753 


85567 


53238 


84650 


54708 


83708 


56.60 


82741 


5o 


II 


50277 


86442 


5.778 


8555. 


53263 


84635 


54732 


836g2 


56.84 


82724 


49 


12 


5o3o2 


86427 


5i8o3 


85536 


53288 


846x9 


54756 


83676 


56208 


82708 


48 


i3 


5o327 


86413 


5x828 


8552. 


533.2 


84604 


54781 


83660 


56232 


82692 


47 


U 


5o352 


86398 


5x852 


855o6 


53337 


84588 


54805 


83645 


56256 


82675 


46 


i5 


5o377 


86384 


5x877 


85491 


5336. 


84573 


54829 


83629 


56280 


82659 


45 


i6 


5o4o3 


86369 


51902 


85476 


53386 


84557 


54854 


836.3 


563o5 


82643 


44 


\l 


50428 


86354 


5.927 


8546. 


534.. 


84542 


54878 


83597 


56329 


82626 


43 


50453 


86340 


5X932 


85446 


53435 


84526 


54902 


83581 


56353 
56377 


826.0 


42 


19 


50478 


86325 


5x977 


8543. 


53460 


845.1 


54927 


83565 


82593 


41 


20 


5o5o3 


863x0 


52002 


85416 


53484 


84495 


5495. 


83549 


5640. 


82577 


40 


21 


5o528 


86295 
8628X 


52026 


85401 


53509 


84480 


54975 


83533 


56425 


8256i 


39 


22 


5o553 


52o5i 


85385 


53534 


84464 


54999 


835x7 


56449 


82544 


38 


23 


50578 


86266 


52076 


85370 


53558 


84448 


55024 


83 5o. 


56473 


82328 


37 


24 


5o6o3 


8625x 


52IOI 


85355 


53583 


84433 


55048 


83485 


56497 
5652. 


823X1 


36 


23 


50628 


86237 


52x26 


85340 


53607 


84417 


55072 


8346q 


82495 


35 


26 


5o654 


86222 


52x5x 


85325 


53632 


84402 


55097 


83453 


56545 


82478 


34 


27 


50679 


86207 


52x75 


853.0 


53656 


84386 


55.2. 


83437 


56569 


82462 


33 


28 


50704 


86x92 


52200 


85294 


53681 


84370 


55.45 


8342. 


56593 


82446 


32 


29 


50729 


86x78 


52225 


85279 


53705 


84355 


55.69 


834o5 


566.7 


82429 


3x 


3o 


50754 


86x63 


5225o 


85264 


53730 


84339 


55194 


83389 


5664. 


824.3 


3o 


3i 


50779 


86x48 


52275 


85249 


53754 


84324 


552x8 


83373 


56665 


82396 


2Q 


32 


50804 


86x33 


52299 


85234 


53779 


84308 


55242 


83356 


56689 


82380 


28 


33 


50829 


86x19 


52324 


852.8 


53804 


84292 


55266 


83340 


567.3 


82363 


27 


34 


5o854 


86x04 


52349 


852o3 


53828 


84277 


5529X 


83324 


56736 


82347 


26 


35 


50879 


86089 


52374 


85.88 


53853 


84261 


553x5 


833o8 


56760 


82330 


25 


36 


50904 


86074 


gs 


85.73 


53877 


84245 


55339 
55363 


83292 


56784 


823.4 


24 


ll 


50929 


86059 


85x57 


53902 


84230 


83276 


568o8 


till] 


23 


50954 


86045 


52448 


85.42 


53926 


84214 


55388 


83260 


56832 


22 


39 


50979 


86o3o 


52473 


85x27 


53951 


84198 
84182 


55412 


83244 


56856 


S2264 


21 


40 


5 1 004 


860 X 5 


52498 


85x12 


53975 


55436 


83228 


56880 


82248 


20 


41 


5io29 


86000 


52522 


85096 
85o8. 


54000 


84167 


55460 


832.2 


56904 


8223X 


;? 


42 


5io54 


85985 


52547 


54024 


841 5. 


55484 


83x95 


56928 


82214 


43 


5io79 


85970 


52572 


85o66 


54049 


84.35 


55509 


83x79 
83.63 


56952 


82198 
82.81 


17 


44 


5iio4 


85956 


52597 


85o5i 


54073 


84.20 


55533 


56976 


16 


45 


51129 


85941 


5262X 


85o35 


54097 


84.04 


55557 


83x47 


57000 


82x65 


i5 


46 


5u54 


85926 


52646 


85020 


54122 


84088 


55581 


83i3x 


57024 


82148 


14 


s 


5ii79 


II 


5267X 


85oo5 


54146 


84072 


556o5 


83xx5 


57047 


82X32 


i3 


5i2o4 


52696 


84989 


541 7 1 


84057 


55630 


lit 


5707X 


82. x5 


X2 


i^ 


51229 


52720 


84974 


54x95 


84041 


55654 


57095 


82098 
82082 


II 


5o 


5i254 


85866 


52745 


84959 
84943 


54220 


84025 


55678 


83o66 


57119 
57.43 


10 


5i 


5x279 


85851 


52770 


54244 


84009 


55702 


83o5o 


82065 


9 
8 


52 


5i3o4 


85836 


52794 


84928 


54269 


83994 


55726 


83o34 


57.67 


82048 


53 


5i329 


85821 


528x9 


849.3 
84897 


54293 


83978 


55750 


83oi7 


57.9. 


82032 


7 


^^ 


5i354 


858o6 


52844 


54317 


83962 


55775 


83oo. 


572.5 


820x5 


6 


55 


5x379 


85792 


52869 


84882 


54342 


83946 


55799 


82985 


57238 


i:??? 


5 


56 


5i4o4 


85777 


52893 


84866 


54366 


83930 


55823 


82969 


57262 


4 


^2 


51429 


85762 


52918 


8485. 


54391 


t£ 


55847 


82953 


57286 


8.965 


3 


58 


51454 


85747 


52943 


84836 


54415 


5587X 


82936 


573.0 


81949 


2 


5g 
M 


5x479 

C.S. 


85732 
S. 


52967 


84820 


54440 
C.S. 


55895 


82920 


57334 
C. S. 


8x932 

s. 


"M 


C.S. 


S. 


s. 


C.S. 


S. 


59 Depr. 


58 Beg. 


57 Beg, i 


56 Deg. 1 


55 Deg. 



70 



A TABLE OF NATURAL SINES. 



1 
M 




85 Deg. 


86 Deg. 


37 Deg. 


88 Deg. 


89 Deg. 




S. 1 c. s. 

57358; 81915 


S. 


G. S. 


S. 


C. S. 


S. 


C. S. 


S. 


C. S. 


M 


58779 


80902 


60182 


79864 


6,^ 


7880. 


62932 


Tnis 


60 


I 


5738 


8.899 


58802 


80885 


6o2o5 


79846 


61589 


78783 


62955 


77696 


59 


2 


5740; 


8.882 


58826 


80867 


60228 


79829 


61612 


78765 


62977 


77678 


58 


3 


5742^ 


8.865 


58849 


8o85o 


6o25i 


7981. 


6i635 


78747 


63ooo 


77660 


57 


4 


57453 


8.848 


58873 


80833 


60274 


79793 


6.658 


78729 


63022 


77641 


56 


5 


57477 


8.832 


58896 


808.6 


60298 


79776 


6168. 


78711 


63045 


77623 


55 


6 


57501 


8i8i5 


58920 


80799 


6o32i 


79758 


61704 


78694 


63o68 


77605 


54 


7 


57524 


8.798 


58943 


80782 


60344 


79741 


61726 


78676 


63090 


77586 


53 


8 


57548 


81782 


58967 


80765 


60367 


79723 


61749 


78658 


63. .3 


77568 


52 


9 


57572 


81765 


58990 


80748 


60390 


79706 


6.772 


78640 


63.35 


77550 


5i 


10 


57596 


1 81748 


590.4 


80730 


60414 


79688 


61795 


78622 


63,58 


77531 


5o 


n 


576,9 
57643 


1 8173. 


59037 


807.3 


60437 


79671 


61818 


78604 


63 1 80 


773.3 


49 


12 


i 8.714 


59061 


80696 


60460 


79653 


6.841 


78586 


63203 


77494 


48 


i3 


57667 


8.698 


59084 


80679 


60483 


79635 


61864 


78568 


63225 


77476 


47 


14 


57691 


8168. 


59.08 


80662 


6o5o6 


79618 


61887 


78550 


63248 


77458 


46 


i5 


577.5 


81664 


5913. 


80644 


60529 


79600 


61909 


78532 


6327. 


77439 


45 


i6 


57738 


8.647 


59.54 


80627 


6o553 


79583 


■61932 


785.4 


63293 


77421 


44 


17 


57762 


8.63. 


59,78 


806,0 


60576 


79565 


61955 


78496 


633.6 


77402 


43 


18 


57786 


81614 


5920. 


80593 


60599 


79547 


61978 


78478 


63338 


77384 


42 


19 


578.0 


'sMl 


59225 


80576 


60622 


79530 


62001 


78460 


6336. 


77366 


41 


20 


57833 


59248 


8o558 


60645 


79512 


62024 


78442 


63383 


77347 


40 


21 


'A^^ 


8.563 


59272 


8o54i 


60668 


79494 


62046 


78424 


63406 


77329 


li 


22 


5788. 


8 1 546 


59295 


8o524 


60691 


79477 


62069 


78405 


63428 


77310 


23 


57904 


8i53o 


593.8 


8o5o7 


607,4 


79459 


62092 


78387 


6345. 


77292 


37 


24 


57928 


8i5i3 


59342 


80489 


60738 


79441 


62, ,5 


78369 


63473 


77273 


36 


25 


57952 


81496 


59365 


80472 


6076, 


79424 


62i38 


7835. 


63496 


77255 


35 


26 


57976 


81479 


59389 


80455 


60784 


79406 


62160 


78333 


635,8 


77236 


34 


27 


57999 


81462 


59412 


80438 


60807 


79388 


62183 


783.5 


63540 


77218 


33 


28 


58023 


8.445 


59436 


80420 


6o83o 


79371 


62206 


78297 


63563 


77199 


32 


29 


58047 


81428 


59459 


80403 


6o853 


79353 


62229 


78279 


63585 


77.8. 


3i 


3o 


58070 


81412 


59482 


8o386 


60876 


79335 


6223, 


78261 


636o8 


77.62 


3o 


3i 


58094 


81395 


59506 


8o368 


60899 


79318 


62274 


78243 


63630 


77144 


29 


32 


D8i,8 


81378 


59529 


8o35, 


60922 


79300 
79282 


62297 


78225 


63653 


77.25 


28 


33 


58.41 


8.36. 


59552 


80334 


60945 


62320 


78206 


63675 


77107 


27 


34 


58.65 


8.344 


59576 


8o3i6 


60968 


79264 


62342 


78.88 


63698 


77088 


26 


35 


58.89 


81327 


59399 


80299 


60991 


79247 


62365 


78.70 


63720 


77070 


23 


36 


58212 


8i3.o 


59622 


80282 


6.0,5 


79229 


62388 


78,52 


63742 


77o5. 


24 


ll 


58236 


8.293 


59646 


80264 


6io38 


79211 


62411 


78,34 


63765 


77033 


23 


58260 


81276 


59669 


80247 


6.06. 


79193 


62433 


78.. 6 


63787 


77014 


22 


39 


58283 


81259 


59693 


8o23o 


6.084 


79176 


62456 


78098 


638.0 


76996 


21 


40 


58307 


81242 


597.6 


80212 


61.07 


791 58 


62479 


78079 


63832 


76977 


20 


41 


58330 


8.225 


59739 


80,95 


6.i3o 


79,40 


62502 


78061 


63854 


76959 


\i 


42 


58354 


81208 


59763 


80.78 


6.. 53 


79,22 


62J24 


7S043 


63877 


76940 


43 


58378 


81.91 


59786 


80.60 


6.. 76 


79,05 


62547 


78025 


63899 


7692. 


17 


44 


5840. 


8. .74 


59809 


80,43 


6.. 99 


79087 


62570 


78007 


63922 


76903 


16 


45 


58425 


8.. 57 


59832 


80.25 


61222 


79069 


62592 


77988 


63944 


76884 


i5 


46 


58449 


8.140 


5o856 


80.08 


6.245 


79o5i 


62615 


77970 


68966 


76866 


14 


47 


58472 


81123 


59879 


8009, 


6.268 


79033 


62638 


77952 


68989 


76847 


i3 


48 


58496 


8.106 


59902 


80073 


6129, 


790,5 


62660 


77934 


6401. 


76828 


12 


49 


585 19 


81089 


59926 


8oo56 


6.3.4 


789L 


62683 


779.6 


64033 


768.0 


I . 


5o 


58543 


81072 


59949 


8oo38 


6.337 


62706 


77897 


64056 


76791 


.0 


5i 


58567 


8io55 


59972 


80021 


6.36o 


78962 


62728 


77879 


64078 


76772 


9 


52 


58590 


8.o38 


59995 


8ooo3 


6.383 


78944 


6275. 


7786, 


64100 


76754 


8 


53 


586 1 4 


8.02. 


60019 


79986 


6.406 


78926 


62774 


77843 


64123 


76735 


7 


54 


58637 


81004 


60042 


79968 


61429 


78908 


62796 


77824 


64145 


76717 


6 


55 


5866. 


80987 


6oo65 


7995. 


6145. 


7889, 


628.9 


77806 


64167 


76698 


5 


56 


58684 


80970 


60089 


79934 


61474 


78873 


62842 


77788 


64190 


76679 


4 


u 


58708 


80953 


60, .2 


799,6 


6.497 


78855 


62864 


77769 


64212 


76661 


3 


5873. 


80936 


6oi35 


79899 


6.520 


78837 


62887 


77751 


64234 


76642 


2 


59 

M 


58755 


80919 
S. 


60, 58 


7988, 
S. 


6 1 543 


78819 
S. 


62909 

c."s. 


77733 
S. 


64256 
C. S. 1 


76623 

S. 


1 
M 


C. S. 


C. S. 


C. S. i 


54 De^. 1 


53 Deg. 1 


52 Deg. 


51 Deg. 1 


50 Deg. 1 



A TABLE OF NATURAL SINES, 



M 




40 Deg. 


41 Deg. 


42 Deg. 


1 43 Deg. 


44 D^cf. 


M 

60 


S. 


C. S. 


S. 
656o6 


1 C. S. 
' 75471 


S. 


C.S. 


S. 


C.S. 


bgm 


|C.S. 
71934 


64279 


76604 


66913 


743x4 


68200 


73i3S 


I 


64301 


76586 


60628 


75452 


66935 


74295 


68221 


73116 


69487 


71914 


59 


2 


64323 


76567 


65650 


75433 


66956 


74276 


68242 


73096 


69508 


71894 


58 


3 


64346 


76548 


65672 


70414 


66978 


74256 


68264 


73076 


69529 


71873 


37 


4 


64368 


76530 


65694 


75395'! 66999 


74237 


68285 


73o56 


69549 


71853 


56 


5 


64390 


765 II 


65716 


75375![ 67021 


74217 


683o6 


73o36 


69570 


^ 71833 


55 


6 


64412 


76492 


i 65738 


70356 


67043 


74198 


68327 


73016 


69O91 


! 7l8l3 


54 


7 


64435 


76473 


65739 


75337 


67064 


74178 


68349 


72996 


696.2 


i 71192 


53 


8 


64457 


76455 


65781 


75318 


67086 


74159 


68370 


72976 


69633; 71772 


52 


9 


64479 


76436 


658o3 


75209 
70280 


67107 


74139 


68391 


72957 


69654 


71732 


5i 


10 


64501 


XI 


65825 


67129 


74120 


68412 


72937 


69675 


71732 


5o 


II 


64324 


65847 


75261 


67i5i 


74100 


68433 


72917 
72897 


69696 
69717 


71711 


S 


12 


64546 


76380 


60869 


75241 


67172 


74080 


68455 


71691 


i3 


64568 


7636i 


65891 


75222 


67194 


74061 


68476 


72877 


69737 


71671 


47 


14 


64590 


76342 


65913 


75203 


67210 


74041 


68497 


72807 


69758 


7i65o 


46 


i5 


64612 


76323 


65935 


75184 


67237 


74022 


68018 


72837 


69779 


7i63o 


45 


i6 


64635 


76304 


65956 


75i65 


67258 


74002 


68539 


72817 


69800 


71610 


44 


n 


64657 


76286 


65978 


75i46 


67280 


73983 


68561 


72797 


69821 


71590 


43 


i8 


64679 


76267 


66000 


75126 


67301 


73963 


68582 


72777 


69842 


71569 


42 


19 


64701 


76248 


66022 


75107 


67323 


73944 


686o3 


72757 


69862 


71549 


41 


20 


64723 


76229 


66044 


75088 


67344 


73924 


68624 


72737 


69883 
69904 


71529 


40 


21 


64746 


76210 


66066 


75069 


67366 


73904 


68645 


72717 


7i5o§ 


ll 


22 


64768 


76192 


66088 


75o5o 


67387 


73885 


68666 


72697 


69925 


71488 


23 


64790 


76173 


66109 


75o3o 


67409 


73865 


68688 


72677 


69946 


71468 


37 


24 


64812 


76154 


661 3 1 


7501 1 


67430 


73846 


68709 


72657 


69966 


71447 


36 


25 


64834 


76135 


66 1 53 


74992 


67452 


73826 


68730 


72637 


69987 


71427 


35 


26 


64856 


76116 


66175 


74973 


67473 


73806 


68751 


72617 


70008 


71407 


34 


^l 


64S78 


76097 


66197 
66218 


74953 


67495 


73787 


68772 


72597 


70029 


71386 


33 


28 


64901 


76078 


74934 


67516 


73767 


68793 


72577 


70049 


71366 


32 


29 


64923 


76059 


66240 


74915 


67538 


73747 


68814 


72557 


70070 


71343 


3i 


3o 


64945 


76041 1 


66262 


74896 


67509 


73728 


68835 


72537 


70091 


71325 


3o 


3i 


64967' 


76022 


66284 


74876 


67580 


73708 


68857 
68878 


72517 


70112 


7i3o5 


S 


32 


64989* 


76003 


663o6 


74857 


67602 


73688 


72497 


70i32 


71284 


33 


65oii 


759841 


66327 


74838 


67623 


73669 


68899 


72477 


70153 


71264 


2 


34 


65o33 


75965 


66349 


74818 


67645 


73649 


68920 


72457 


70174 


71243 


^35 


65o55 


75946 


66371 


74799 


67666 


73629 


68g4i 


72437 


70193 


71223 


25 


36 


65077 


75927, 


66393 


74780 


67688 


73610 


68962 


72417 


70213 


71203 


24 


37 


65o99 


t0^ 


66414 


74760 


67709 


73090 


68983 


72397 


70236 


71182 


23 


38 


65l22 


66436 


74741 


67730 


73570 


69004 


72377 


70237 


71162 


22 


39 


65J44 


75870! 

75851 


66458 


74722 


67752 


73551 


69025 


72337 


70277 


71141 


21 


40 


65i66 


66480 


74703 


67773 


73531 


69046 


72337 


70298 


71121 


20] 


41 


65:88, 


75832 


66501 


74683 


67795 


73511 


69067 


72317 


70319 


71100 




42 


65210 


758.3i 


66523 


74664 


67816 


73491 


69088 


72297 


70339 


71080 


6 1 


43 


65232 


75794) 


66545 


74644 


67837 


73472 


69109 


72277 


7o36o 


71009 


17 


44 


65254 


75775; 


66066 


74625 


67859 


73452 


69130 


72257 


7o38i 


71039 


16 


45 


65276: 


75756! 


66588 


74606 


67880 


73432 


69151 


72236 


70401 


71019 


13 


46 


65298' 


75738' 


66610 


74586 


67901 


73412 


69172 


72216 


70422 


70998 


14 


47 


65320 


75719 


66632 


74567 


67923 


73393 


69193 


72196 


70443 


70978 


i3 


48 


65342 


?SJ 


66653 


7454s 


67944 


73373 


69214 


72176 


70463 


70937 


12 


49 


65364 


66675 


74528 


67965 


73353 


69235 


72i56 


70484 


70937 
70916 


II 


5o 


65386, 


75661 


66697 


74509 


as 


73333 


69256 


72i36 


7o5o5 


10 


5i 


654o8 


75642: 


66718 


74489 


73314 


69277 


72116 


70525 


70896 


I 


52 


6543o 


75623i 


66740 


74470 


68029 


73294 


69298 


72095 


70546 


70875 


53 


654021 


7 5604 1 


66762 


7445 1 


68o5i 


73274 


69319 


72070 


70567 


70855 


7 


54 


65474J 


755851 


66783 


7443: 


68072 


73254 


69340 


72055 


70587 


70834 


6 


55 


65496 


75566 


66800 


74412 


68093 


73234 


69361 


72035 


70608 


70813 


5 


56 1 


655i8 


75547' 


66827 


74392 


68ii5 


732i5 


69382 


72015 


70628 


70793 


4 


ll ! 


65540 


755281 


66848 


74373 


68i36 


73195 


69403 


71990 


70649 


70772 


3 


f i 


65562 


730091 


66870 


74353 


68107 


73175 


69424 


71974 


70670 


70752 


2 


59 ! 


65584 


75490 


66891 


74334 


68179 


73i55 


69445 


71954 


70690 


70731 


I 


60 

i 


656o6 
C. S. 


75471 
S. 


66913 


74314 


68200 


73i35 


69466 
C.S. 


71934 

S. 


707 1 1 
C.S. 


70711 
S. 





C. s. 1 


S. 


C. S. 


S. 


49 1 


eg. 1 


48 Deg. 1 


47 Deg. 1 


46 Deg. ! 


45 Deg. 1 



travetjst; taklf. 



a 

p 

B 
§ 


iDeg. 


iDeg. 


1 Deg. 


1 


Lat. 


Dep, 
0.00 


Lat. 


Dep. 

~o:oi 


Lat. 


Dep. 


1.00 


1.00 


1.00 


0.01 


2 


2.00 


0.01 


2.00 


0.02 


2.00 


0.03 


2 


3 


3.00 


0.01 


3.00 


0.03 


3.00 


0.04 


3 


4 


4.00 


0.02 


4.00 


0.03. 


4.00 


0.05 


4 


5 


5.00 


0.02 


5.00 


0.04 


5.00 


0.07 


5 


6 


6.00 


0.03 


6.00 


0.05 


6.00 


0.08 


6 


7 


7.00 


0.03 


7.00 


0.06 


7.00 


0.09 


7 


8 


8.00 


0.03 


8.00 


0.07 


8.00 


0.10 


8 


9 


9.00 


0.04 


9.00 


0.08 


9.00 


0.12 


9 


10 


10.00 
11.00 


0.04 
0.05 


10.00 
11.00 


0.09 
0.10 


10.00 
11.00 


0.13 

0.14 


10 
if 


11 


12 


12.00 


0.05 1 


12.00 


0.10 


12.00 


0.16 


12 


13 


13.00 


0.06 1 


13.00 


0.11 


13.00 


0.17 


13 


14 


14.00 


0.06 


14.00 


0.12 


14.00 


0.18 


14 


15 


15.00 


0.07 


15.00 


0.13 


15.00 


0.20 


15 


16 


16.00 


0.07 


16.00 


0.14 


16.00 


0.21 


16 


17 


17.00 


0.07 


17.00 


0.15 


17.00 


0.22 


17 


18 


18.00 


08 


18 00 


0.16 


18.00 


0.24 


18 


19 


19.00 


0.08 


19.00 


0.17 


19.00 


0.25 


19 


20 


20.00 


0.09 


20.00 


0.17 


20.00 


0.26 


20 


21 


21.00 


0.09 


21.00 


0.18 


21.00 


0.27 


21 


22 


22.00 


0.10 


22.00 


0.19 


22.00 


0.29 


22 


23 


23.00 


0.10 1 


23.00 


0.20 


23.00 


0..S0 


23 


24 


24.00 


0.10 


24.00 


0.21 


24.00 


0.31 


24 


25 


25.00 


0.11 


25.00 


0.22 


25.00 


0.33 


25 


26 


26.00 


0.11 


26.00 


0.23 


26.00 


0.34 


26 


27 


27.00 


0.12 


27.00 


0.24 


27.00 


0.35 


27 


28 


28.00 


0.12 


28.00 


0.24 


28.00 


0.37 


28 


29 


29.00 


0.13 


29.00 


0.25 


29.00 


0.38 


29 


30 


30.00 


0.13 


30.00 


0.26 


30.00 


0.39 


30 


31 


31.00 


0.14 


31.00 


0.27 


31.00 


0.41 


31 


32 


32.00 


0.14 


32.00 


0.28 


32.00 


0.42 


32 


33 


33.00 


0.14 


83.00 


0.29 


33.00 


0.43 


33 


34 


34.00 


0.15 


34.00 


0.30 


34.00 


0.45 


34 


35 


35.00 


0.15 


35.00 


0.31 


35.00 


0.46 


35 


36 


36.00 


0.16 


36.00 


0.31 


36.00 


0.47 


36 


37 


37.00 


0.16 


37.00 


0.32 


37.00 


0.48 


37 


38 


38.00 


0.17 


38.00 


0.33 


38.00 


0.50 


38 


39 


39.00 


0.17 


39.00 


0.34 


39.00 


0.51 


39 


40 
41 


40.00 
41.00 


0.17 
0.18 


40.00 


0.35 
0.36 


40.00 
41.00 


0.52 
0.54' 


40 
41 


41.00 


42 


42.00 


0.18 


42.00 


0.37 


42.00 


0.55 


42 


43 


43.00 


0.19 


43.00 


0.38 


43.00 


0.56 


43 


44 


44.00 


0.19 


44.00 


0.38 


44.00 


0.58 


44 


45 


45.00 


0.20 


45.00 


0.39 


45.00 


0.59 


45 


46 


46.00 


0.20 


46.00 


0.40 


46.00 


0.60 


46 


47 


47.00 


0.21 


47.00 


0.41 


47.00 


0.63 


47 


48 


48.00 


0.21 


48.00 


0.42 


48.00 


0.63 


48 


49 


49.00 


0.21 


49.00 


0.43 


49.00 


0.64 


49 


50 


50.00 


0.22 


50.00 


0.44 


50.00 


0.65 


50 


1 
.2 


Dep. 

891 


Lat. 
Deg. 


Dep. 


Lat. 


Dep. 


Lat. 


1 


89^ 


Deg. 


1 

I 89i 


Deg. 



TRAVERSE TAHLE. 



9. 


iDeg. 


k 


Deg. 


IDeg. 


1 


1 






Lat. 


Dep. 








Lat. 


Dep. 


Lai. 


1 Dep. 




51 


Troo 


0.22 


51.00 


0.45 


51.00 


"0767 


^ 


52 


52.00 


0.23 


52.00 


0.45 


52.00 


0.68 


52 


53 


53.00 


0.23 


53.00 


0.46 


53.00 


0.69 


53 


54 


54.00 


0.24 


54.00 


0.47 


54.00 


0.71 


54 


55 


55.00 


0.24 


55.00 


0.48 


55.00 


0.72 


55 


56 


56.00 


0.24 


56,00 


0.49 


56.00 


0.73 


56 


57 


57.00 


0.25 


57.00 


0.50 


57.00 


0.75 


57 


58 


58.00 


0.25 


58.00 


0.51 


57.99 


0.76 


68 


59 


59.00 


0.26 


59.00 


0.51 


58.99 


0.77 


59 


60 


60.00 


0.26 


6C.00 


0.52 


59.99 


0.79 


60 


61 


61.00 


'0.27 


61.00 


0".53" 


60.99 


0.80 


61 


62 


62.00 


0.27 


62.00 


0.54 


61.99 


0.81 


62 


63 


63.00 


0.27 


63.00 


0.55 


62.99 


0.82 


63 


64 


64.00 


0.28 


64.00 


0.56 


63.99 


0.84 


64 


65 


65.00 


0.28 


65.00 


0.57 


64.99 


0.85 


65 


66 


66.00 


0.29 


66.00 


0.58 


65.99 


0.86 


66 


67 


67.00 


0.29 


67.00 


0.58 


66.99 


0.88 


67 


68 


68.00 


0.30 


68.00 


0.59 


67.99 


0.89 


68 


69 


69.00 


0.30 


69.00 


0.60 


68.99 


0.90 


69 


70 
71 


70.00 
71 .00 


0.31 
0.31 


70.00 
71.00 


0.61 


69.99 


0.92 
0.93 


70 
71 


0.62 


70.99 


72 


72.00 


0.31 


72.00 


0.63 


71.99 


0.94 


72 


73 


73.00 


0.32 


73.00 


0.64 


72.99 


0.96 


73 


74 


74.00 


0.32 


74.00 


0.65 


73.99 


0.97 


74 


75 


75.00 


0.33 


75.00 


0.65 


74.99 


0.98 


75 


76 


76.00 


0.33 


76.00 


0.66 


75.99 


0.99 


76 


77 


77.00 


0..34 


77.00 


0.67 


76.99 


l.Cl 


77 


78 


78.00 


0.34 


78.00 


0.68 


77.99 


1.02 


78 


79 


79.00 


0.34 


79.00 


0.69 


78.99 


1.03 


79 


80 
81 


80.00 


0.35 
0.35 


80.00 
81.00 


0.70 
0.71 


79.99 
80.99 


1.05 


80 
81 


81.00 


1.06 


82 


82.00 


0.36 


82.00 


0.72 


81.99 


1.07 


82 


83 


83.00 


0.36 


83.00 


0.72 


82.99 


1.09 


83 


84 


84.00 


0.37 


84.00 


0.73 


83.99 


1.10 


84 


85 


85.00 


0.37 


85.00 


0.74 


84.99 


1.11 


85 


86 


86.00 


0.38 


86.00 


0.75 


85.99 


1.13 


86 


87 


87.00 


0.38 


87.00 


0.76 


86.99 


1.14 


87 


88 


88.00 


0.38 


88.00 


0.77 


87.99 


1.15 


88 


89 


89.00 


0.39 


89.00 


0.78 


88.99 


1.16 


89 


90 
91 


90.00 
91.00 


0.39 


90.00 
91.00 


0.79 


89.99 
90.99 


1.18 
1.19 


90 

91 


0.40 


0.79 


92 


92.00 


0.40 


92.00 


0.80 


91.99 


1.20 


92 


93 


93.00 


0.41 


93.00 


0.81 


92.99 


1.22 


93 


94 


94.00 


0.41 


94.00 


0.82 


93.99 


1.23 


94 


95 


95.00 


0.41 


95.00 


0.83 


94.99 


1.24 


95 


96 


96.00 


0.42 


96.00 


0.84 


95.99 


1.26 


96 


97 


97.00 


0.42 


97.00 


0.85 


96.99 


1.27 


97 


98 


98.00 


0.43 


98.00 


0.86 


97.99 


1.28 


98 


99 


99.00 


0.43 


99.00 


0.86 


98.99 


1.30 


99 


100 


100.00 


0.44 
Lat. 


100.00 
Dep. 


0.87 
Lat. 


99.99 
Dep. 


1.31 


100 

i 

.2 

o 


Dep, 


Lat. 


89! 


Deg. 


89A Deg. 


39i Deg. 



TRAVF.RSE TABiE. 



1 


1 Deg, 


H Deg. 


11 Deg. 1 


11 Deg. 


1 


Lat. 


Dep. 

6702 


Lat. 


D^p. 


Lat. 1 Dop. ■ 


Lat. 


Dep. 


1.00 


1.00 


0.02 


1.00 


0.03 


1.00 


~~0Ai3 


2 


2.00 


0.03 


2.00 


0.04 


2.00 


0.05 


2.00 


0.06 




3 


3.00 


0.05 


3.00 


0.07 


3.00 


0.08 


3.00 


0.09 


3 


4 


4.00 


0.07 


4.00 


0.09 


4.00 


0.10 


4.00 


0.12 


4 


5 


5.00 


0.09 


5.00 


0.11 


5.00 


0.13 


5.00 


0.15 


5 


6 


6.00 


0.10 


G.OO 


0.13 


6.00 


0.16 


6.00 


0.18 


6 


7 


7.00 


0.12 


7.00 


0.15 


7.00 


0.18 


7.00 


0.21 


7 


8 


8.00 


0.14 


8.00 


0.17 


8.00 


0.21 


8.00 


0.25 


8 


9 


9.00 


0.16 


9.00 


0.20 


9.00 


0.24 


9.00 


0.28 


9 


10 


10.00 


0.17 


10.00 


0.22 


10.00 
11.00" 


0.26 


10.00 


0.31 


10 


11 


H.OO 


0.19 


il.OO 


0.24 


0.28 


10.99 


0.34 


11 


12 


12.00 


0.21 


12.00 


0.26 


12.00 


0.31 


11.99 


0.37 


12 


13 


13.00 


0.23 


13.00 


0.28 


13.00 


0.34 


12.99 


0.40 


13 


14 


14.00 


0.24 


14.00 


0.31 


14.00 


0.37 


13.99 


0.43 


14 


15 


15.00 


0.26 


15.00 


0.33 


14.99 


0.39 


14.99 


0.46 


i5 


16 


16.00 


0.28 


16.00 


0.35 


15.99 


0.42 


15.99 


0.49 


16 


17 


17.00 


0.30 


17.00 


0.37 


16.99 


0.45 


16.99 


0.52 


17 


18 


18.00 


0.31 


18.00 


0.39 


T7.99 


0.47 


17.99 


0.55 


18 


19 


19.00 


0.33 


19.00 


0.41 


18.99 


0..50 


18.99 


0.58 


19 


20 
21 


20.00 I 0.35 1 


20.00 
21 .00 


0.44 
0.46 


19.99 


0.52 
0.55 


19.99 


0.61 


20 


21.00 


0.37 


20.99 


20.99 


0.64 


21 


22 


22.00 


0.38 


21.99 


0.48 


21.99 


0.58 


21.99 


0.67 


22 


23 23.00 


0.40 


22.99 


0.50 


22.99 


0.60 


22.99 


0.70 


23 


24 


24.00 


0.42 


23.99 


0.52 


23.99 


0.63 


23.99 


0.73 


24 


25 


25 . 00 


0.44 


24.99 


0.55 


24,99 


0.65 


24.99 


0.76 


25 


26 


2G.00 


0.45 


25.99 


0.57 


25.99 


0.68 


25.99 


0.79 


26 


27 


27.00 


0.47 


26.99 


59 


26.99 


0.71 


26.99 


0.83 


27 


28 


28.00 


0.49 


27.99 


0.61 


27.99 


0.73 


27.99 


0.86 


28 


29 


29.00 


0.51 


28.99 


0.63 


28.99 


0.76 


28.99 


0.89 


29 


30 
31 


30.00 


0.52 


29.99 
30.99 


0.65 


29.99 
30.99 


0.79 


29.99 
30.99 


0.92 


30 


31.00 


0.54 


0.68 


0.81 


0.95 


31 


32 


32.00 


0.56 


31.99 


0.70 


31.99 


0.84 


31.99 


0.98 


32 


33 ■ 32 . 99 


0.58 


32.99 


0.72 


32.99 


0.86 


32.98 


1.01 


33 


34,33.99 


0.59 


33.99 


0.74 


33.99 


0.89 


33.98 


1.04 


34 


35 


34.99 


0.61 


34.99 


0.76 


34.99 


0.92 


34.98 


1.07 


35 


36 


^5.99 


0.63 


35.99 


0.79 


35.99 


0.94 


35.98 


1.10 


35 


37 


36.99 


0.05 


36.99 


0.81 


36.99 


0.97 


36.98 


1.13 


37 


38 


37.99 


0.66 


37.99 


0.83 


37.99 


0.99 


' 37.98 


1.16 


38 


39 


38.99 


0.68 


38.99 


0.85 


38.99 


1.02 


138.98 


! 1.19 


39 


40 
41 


39.99 
40.99 


0.70 


39.99 


0.87 


39.99 
40.99 


1.05 
1.07 


39.98 
40.98 


, 1 .22 


40 
"41 


0.72 


40.99 


0.89 


1 25 


42 


41.99 


0.73 


41.99 


0.92 


41.99 


1.10 


41.98 


1 28 1 42 


43 


42 . 99 


0.75 


42.99 


0.94 


42.99 


1.13 


42.98 


1.31 43 


44 


43.99 


0.77 


43.99 


0.96 


43.99 


1.15 


43.98 


l.b4 44 


45 


44.99 


0.79 


44.99 


0.98 


44.99 


1.18 


44.98 


1.37 45 


46 


45.99 


0.80 


45.99 


1.00 


45.99 


1.20 


45.98 


1.40 46 


47 


46.99 i 0.82 


46.99 


1.03 


46.99 


1.23 


46.98 


1.44 47 


48 


47.99 0.84 


47.99 


1.05 


47.98 


1.26 


47.98 


1.47 


49 


49 


48.99 


0.86 


48.99 


1.07 


48.98 


1.28 


48.98 


1.50 


49 


50 


49.99 


0.87 


49.99 


1.09 


49.98 


_1-31. 


49.98 
Dep. 


1.53 


50 

5 


a 
.2 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Lat. 


89 Deg. 


881 


Deg. 


881 


Deg. 


88iDeg. 



TRAVERSE TABLE. 



1 

3 
? 

"51 


iDeg. 


U Deg. 


H 


Deg. 


1| Deg. 


D 
s 


Lat. 


Dep. 


Lat. 


Dep. 
1.11 


Lat. 


Dep. 


Lat. 


Dep. 


50.99 


0.89 


50.99 


.=)0.98 


nr34 


"50.W 


1.56 


51 


52 


51.99 


0.91 


51.99 


1.13 


51.98 


1.36 


51.98 


1..59 


52 


53 


52 99 


0.92 


52.99 


1.10 


52 . 98 


1.39 


52.98 


1.62 


53 


54 


53 99 


0.94 


53.99 


1.18 


53 . 98 


1.41 


53.97 


1.65 


54 


55 


54 99 


0.96 


54.91' 


1.20 


54.98 


1.44 


54.97 


1.68 


55 


56 


55.99 


0.98 


55.99 


1.22 


55.98 


1.47 


55.97 


1.71 


56 


57 


56.99 


0.99 


56.99 


1.24 


56 m 


1.49 


56.97 


1.74 


57 


58 


57.99 


1.01 


57.99 


1.27 


h7 . 98 


1.62 


57.97 


1.77 


58 


59 


58.99 


1.03 


58.99 


1.29 


58.98 


1.54 


58.97 


1.80 


59 


60 
61 


59.99 


1.05 


59.99 


1.31 


59.98 


1.67 


69.97 


1.83 


60 


60.99 


1.06 


60.99 


60.98 


1.60 


60.97 


1.86 


61 


62 


61.99 


1.08 


61.99 


1.35 


61.98 


1.02 


61.97 


1.89 


62 


63 


62.99 


1.10 


62.99 


1.37 


62.98 


1.65 


62.97 


1.92 


63 


64 


63.99 


1.12 


63.98 


1.40 


63.98 


1.68 


63.97 


1.95 


64 


65 


64.99 


1.13 


64.98 


1.42 


64.98 


1.70 


64.97 


1.99 


65 


66 


65.99 


1.15 


65.98 


1.44 


85.98 


1.73 


05.97 


2.02 


66 


67 


66.99 


1.17 


66.98 


1.46 


66.98 


1.75 


66.97 


2.05 


67 


68 


67.99 


1.19 


67.98 


1.48 


67.98 


1.78 


67.97 


2.08 


68 


69 


68.99 


1.20 


68.98 


1.51 


68.98 


1.81 


68 97 


2.11 


69 


70 
71 


69.99 
70.99 


1.22 


69.98 


1..53 


69.98 


1.83 


69.97 


2.14 


70 
71 


1.24 


70.98 


1..55 


70.98 


1.86 


70.97 


2.17 


72 


71.99 


1.26 


71.98 


1.57 


71.98 


1.88 


71.97 


2.20 


72 


73 


72.99 


1.27 


72.98 


1.59 


72.97 


1.91 


72.97 


2.23 


73 


74 


73.99 


1.29 


73.98 


1.61 


73.97 


1.94! 


73.97 


2.26 


74 


75 


74.99 


1.31 


74.98 


1.64 


74.97 


1.961 


74.97 


2.29 


75 


76 


75.99 


1.33 


75.98 


1.66 


75.97 


1.99 


75.96 


2.32 


76 


77 


76.99 


1.34 


76.98 


1.68 


76.97 


2.02 


76.96 


2.35 


77 


78 


77.99 


1.36 


77.98 


1.70 


77.97 


2.04 


77.96 


2.38 


78 


79 


78.99 


1..38 


78.98 


1.72 


78.97 


2.07 


78.96 


2.41 


79 


80 
81 


79.99 
80.99 


1.40 


79.98 
80.98 


1.75 


79.97 


2.09 


79.96 


2.44 


80 


1.41 


1.77 


80.97 


2.12 


80.96 


2.47 


81 


82 


81.99 


1.43 


81.98 


1.79 


81.97 


2.15 


81.96 


2.50 


82 


83 


82.99 


1.45 


82.98 


1.81 


82.97 


2.17 


82.96 


2.53 


83 


84 


83.99 


1.47 


83.98 


1.83 


83.97 


2.20 


83.96 


2.57 


84 


85 


84.99 


1.48 


84.98 


1.85 


84.97 


2.23 


84.96 


2.00 


85 


86 


85.99 


1..50 


85.98 


1.88 


85.97 


2.26 


85.96 


2.63 


86 


87 


86.99 


1.52 


86.98 


1.90 


86.97 


2.28 


86.96 


2.66 


87 


88 


87.99 


1.54 


87.98 


1.92 


87.97 


2.30 


87.96 


2.69 


88 


•89 


88.99 


1.55 


88.98 


1.94 


88.97 


2.33 


88.96 


2.72 


89 


90 
91 


89.99 


1.57 


89.98 


1.96 
1.99 


89.97 


2.36 


89.96 


2.75 
' 2.78 


90 
91 


90.99 


1.59 


90.98 


90.97 


2.38 


90.96 


92 


91.99 


1.61 


91.98 


2.01 


91.97 


2.41 


91.98 


2.81 


92 


93 92.99 


1.62 


92.98 


2.03 


92.97 


2.43 


92.96 


2.84 


93 


94 93.99 


1.64 


93.98 


2.05 


93.97 


2.46 


93.96 


2.87 


94 


95 94.99 


1.66 


94.98 


2.07 


94.97 


2.49 


94.96 


2.90 


95 


96 


95.99 


1.68 


95.98 


2.09 


95.97 


2.51 


95.96 


2.94 


96 


97 


96.99 


1.69 


96.98 


2.12 


96.97 


2.. 54 


96.95 


2.96 ; 97 


98 


97.99 


1.71 


97.98 


2.14 


97.97 


2.57 


97.95 


2.99 98 


99 


98.98 


1.73 


98.98 


2.16 


98.97 


2.59 


98.95 


3.02 99 


100 

Q 


99.98 


1.75 


1 99.98 


2.18 


99.97 


2.62 


99.95 


3.05 |lO0 


Dep. 


,L... 


Dep. 


Lat. 


Dep. 
88X 


Lat. 
Deg. 


Dep. 


Lat. 


\i 


89 Deg. 


881 Deg. 

1 


8Bi 


Deg. 


li 

JQ 



TRAVERSE TABLE. 



1 

r 


2Deg. 


2^ Deg. 


2i Deg, 


21- Deg. 


m 
1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1.00 


0.03 


1.00 


0,04 


1.00 


0.04 


1.00 


0.05 


1 


2 


2.00 


0.07 


2.00 


0.08 


2.00 


0.09 


2.00 


0.10 


2 


3 ! 3.00 


0,10 


3.00 


0.12 


3.00 


0,13 


3.00 


0.14 


3 


4 


4.00 


0.14 


4.00 


0.16 


4.00 


0.17 


4.00 


0.19 


4 


5 


5.00 


0.17 


5.00 


0.20 


5.00 


0,22 


4.99 


0.24 5 8 


6 


6.00 


0.21 


6.00 


0.24 


5.99 


0.26 


5,99 


0.29 


6 


7 


7.00 


0.24 


6.99 


0.27 


6.99 


0.31 


6,99 


0.34 


7 


8 


7.99 


0.28 


7.99 


0.31 


7.99 


0.35 


7.99 


0.38 


8 


9 


8.99 


0.31 


8.99 


0.35 


8.99 


0,39 


8.99 


0.43 


9 


10 


9.99 


0.35 


9.99 


0.39 


9.99 


0,44 


S.99 


0.48 


10 
if 


11 


10.99 


0.38 


10.99 


0.43 


10.99 


0,48 


10.99 


0.53 


12 


11.99 


0.42 


11.99 


0.47 


11.99 


0.52 


11.99 


0.58 


12 


13 


12.99 


0.45 


12.99 


0.51 


12.99 


0.57 


12.99 


0.62 


13 


14 


13.99 


0.49 


13.99 


0.55 


13.99 


0.61 


13.98 


0.67 


14 


15 


14.99 


0.52 


14.99 


0.59 


14.99 


0.65 


14.98 


0.72 


15 


16 


15.99 


0.56 


15.99 


0.63 


15.99 


0.70 


15.98 


0.77 


16 


17 


16.99 


0..39 


16.99 


0.67 


16.98 


0.74 


16.98 


0.82 


17 


18 


17.99 


0.63 


17.99 


0.71 


17.98 


0,79 


17.98 


0.86 


18 


19 


18.99 


0.66 


18.99 


0.75 


18.98 


0.83 


18.98 


0.91 


19 


20 


19.99 


0.70 


19.98 


0.79 


19.98 


0.87 


19.98 


0.96 


20 


21 


20.99 


0.73 


20 . 98 


0.82 


20.98 


0.92 


20.98 


1.01 


21 


22 21.99 


0.77 


21.98 


0.86 


21.98 


0.96 


21.97 


1.06 


22 


23 22.99 


O.bO 


22 . 98 


0.90 


22.98 


1.00 


22.97 


1.10 


23 


24 123.99 


0.84 


23.98 


0.94 


23.98 


1.05 


23.97 


1.15 


24 


25 24.98 


0.87 


24.98 


0.98 


24.98 


1.09 


24.97 


1.20 


25 


26 25. OH 


0.91 


25.98 


1.02 


25.98 


1.13 


125.97 


1.25 


26 


27 26.98 


0.94 


26.98 


1.06 


26.97 


1.18 


26.97 


1.30 


27 


28 127.98 


0.98 


27.98 


1.10 


27.97 


1.22 


27.97 


1.34 


28 


29 128.98 


1.01 


28.98 


1.14 


28.97 


1.26 


28.97 


1..39 


29 


30 1 29.98 


1.05 


29.98 


1.18 


29.97 


1.31 


29.97 


1.44 


30 

31 


31 30.98 


1.08 


30.98 


1.22 


30.97 


1.35 


130.96 


1.49 


32 31.98 


1.12 


31.98 


1.26 


31.97 


1,40 


31.96 


1..54 


32 


33 32.98 


1,15 


32.97 


1,30 


32.97 


1,44 


32.96 


1.58 


33 


34 33.98 


1.19 


33.97 


1.33 


33.97 


1.48 


33.96 


1.63 


34 


35 


34.98 


1.22 


34.97 


1.37 


34.97 


1.53 


34.96 


1.68 


35 


36 


35.98 


1.26 


35.97 


1.41 


35.97 


1.57 


35.96 


1.73 


36 


37 


36.98 


1.29 


36.97 


1.45 


36.96 


1.61 


36.96 


1.78 


37 


38 


37.98 


1.33 


37.97 


1.49 


37.96 


1,66 


37.96 


1.82 


38 


39 


38.98 


1,36 


38.97 


1.53 


38.96 


1,70 


38.96 


1.87 


39 


40 
41 


39.98 
40.98 


1.40 
1.43 


39.97 


1,57 


39.96 


1.75 


39.95 


1.92 


40 
^41 


40,97 


1.61 


40.96 


1.77 


40.95 


1.97 


42 


41.97 


1.47 


41,97 


1.65 


41,96 


1.83 


41.95 


2.02 


42 


43 


42.97 


1.50 


42.97 


1,69 


42,96 


1.88 


42.95 


2.06 


43 


44 


43.97 


1.54 


43.97 


1,73 


43.96 


1.92 


43.95 


2.11 


44 


45 


44.97 


1,57 


44.97 


1.77 


44.96 


1,96 


44.95 


2.16 


45 


46 


45.97 


1.61 


45.96 


1,81 


45.96 


2.01 


45.95 


2.21 


46 


47 


46.97 


1,64 


46.96 


1,85 


46.96 


2,05 


46.95 


2.25 


47 


48 


47.97 


1,68 


47.96 


1.88 


47.95 


2,09 


47.95 


2.30 


48 


49 


48.97 


1.71 


48.96 


1.92 


48.95 


2.14 


48.94 


2.35 


49 


50 149.97 


1.74 


49.96 


1^ 


49.95 


2.18 


49.94 


2.40 


_50 

© 

s 


8 


Dep 


Lat. 


Dep. 


Lat, 


Dep. 


Lat. 


Dep. 


Lat. 


5 


88 1 


3eg. 


871 Deg. 


87| 


Deg. 


87i Deg. 



TRAVERSE TABLE. 



1 

"5l 


2 Deg. 2i Deg. 


2^ Deg. 


21 Deg. 


111- 


Lat. 


Dep. Lat. 


Dep. 


1- " 


Dep. 


Lat. 


Dep. 


50.97 


1.78 50.96 


2.00 


50.95 


2.22 


50.94 


2.45 


52 


51.97 


1.81 51.96 


2.04 


51.95 


2.27 


51.94 


2.50 


52 


53 


52.97 


1.85 52.96 


2.08 


52.95 


2.31 


52.94 


2.54 


I 53 


54 


53.97 


1.88 1 53.96 


2.12 


53.95 


2.36 


j 53.94 


2.59 


54 


65 


54.97 


1.92 1 54.96 


2.16 


54.95 


2.40 


54.94 


2.64 


55 


56 


55.97 


1.95 il 55.96! 2.20 


55.95 


2.44 


55.94 


2.69 


! 56 


57 


56.97 


1.99 , 56.96 1 2.24 


56.95 


2.49 


56.93 


2.73 


57 


58 


57.96 


2.02 


i 57.96 2.28 


57.94 


2.53 


57.93 


2.78 


58 


59 


58.96 


2.06 


58.95! 2.32 


58.94 


2.57 


58.93 


2.83 


59 


60 
61 


59.96 


2.09 


59.95 j 2.36 


59.94 


2.62 
2.66 


59.93 


2.88 


60 
-61 


60.96 


2.13 


60,95 2.39 


60.94 


60.93 


2.93 


62 


61.96 


2.16 


61.951 2.43 


61.94 


2.70 


61.93 


2.97 


62 


63 


62.96 


2.20 


62.95 1 2.47 


62.94 


2.75 


62.93 


3.02 


63 


64 


63.96 


2.23 


63.95! 2.51 


63.94 


2.79 


63.93 


3.07 


64 


65 


64.06 


2.27 


64.95: 2.55 


164.94 


2.84 


64.93 


3.12 


65 


66 


65.96 


2.30 


65.95! 2. .59 


165.94 


2.88 


65.92 


3.17 


66 


67 


06.96 


2.34 


66.95 


2.63 


66.94 


2.92 


66.92 


3.21 


67 


68 


67.96 


2.37 


67.95 


2.67 


67.94 


2.97 


67.92 


3.26 


68 


69 


68.96 


2.41 


68.95 


2.71 


68.93 


3.01 


68.92 


3.31 


69 


70 
71 


69.96 


2.44 


69.95 1 2.75 


69.93 


3.05 


69.92 


3.36 


70 

71 


70.96 


2.48 


70.95 2.79 


70.93 


3.10 


70.92 


3.41 


72 


71.96 


2.51 


71.94 2.83 


71.93 


3.14 


71.92 


3.45 


72 


73 


72.96 


2.55 


72.94 2.87 


72.93 


3.18 


72.92 


3.50 


73 


74 


73.95 


2.58 


73.94 1 2.91 


73.93 


3.23 


73.91 


3.55 


74 


75 


74.95 


2.62 


74.94 


2.94 


74.93 


3.27 


74.91 


3.60 


75 


76 


75.95 


2.65 


75.94 


2.98 


75.93 


3.31 


75.91 


3.65 


76 


77 


76.95 


2.69 


76,94 


3.02 


76.93 


3.36 


76.91 


3.70 


77 


78 


77.95 


2.72 


77.94 


3.06 


77.93 


3.40 


77.91 


3.74 


78 


79 


78.95 


2.76 


78.94 


3.10 


78.92 


3.45 


78.91 


3.79 


79 


80 
81 


79.95 


2.79 


79.94 


3.14 


79.92 


3.49 


79.91 


3.84 
3.89 


80 
81 


80.95 


2.83 


80.94 


3.18 


80.92 


3.53 


80.91 


82 


81.95 


2.86 


81.94 


3.22 


81.92 


3.58 


81.91 


3.93 


82 


83 


82.95 


2.90 


82.94 


3.26 


82.92 


3.62 


82.90 


3.98 


83 


84 


83 . 95 


2.93 


83.94 


3.30 


83.92 


3.66 


83.90 


4.03 


84 


85 


84.95 


2.97 


84.93 


3.34 


84.92 


3.71 


84.90 


4.08 


85 


86 


85.95 


3.00 


85.93 


3.38 


85.92 


3.75 


85.90 


4.13 


86 


87 


86.95 


3.04 


86.93 


3.42 


86.92 


3.79 


86.90 


4.17 


87 


88 


87.95 


3.07 


87.93 


3.45 


87.92 


3.84 


87.90 


4.22 


88 


89 


88.95 


3.11 


88.93 


3.49 


88.92 


3.88 


88.90 


4.27 


89 


90 
91 


89.95 


3.14 


89.93 


3.53 


89.91 


3.93 


89.90 


4.32 


90 
91 


90.95 


3.18 


90.93 


3.57 


90.91 


3.97 


90.90 


4.37 


92 91.94 


3.21 


91.93 


3.61 


91.91 


4.01 


91.89 


4.41 


92 


93 92.94 


3.25 


92.93 


3.65 


92.91 


4.06 


92.89 


4.46 


93 


94 


93.94 


3.28 


93.93 


3.69 


93.91 


4.10 


93.89 


4.51 


94 


95 


94.94 


3.32 


94.93 


3.73 


94.91 


4.14 


94.89 


4.56 


95 


96 


95.94 


3.35 


95.93 


3.77 


95.91 


4.19 


95.89 


4.61 


96 


97 


96.94 


3.39 


96.93 


3.81 


96.91 


4.23 


96.89 


4.65 


97 


98 


97.94 


3.42 


97.92 


3.85 


97.91 


4.27 


97.89 


4.70 


98 


99 


98.94 


3.46 


98.92 


3.89 


98.91 


4.32 


98.89 


4.75 


99 


100 


99.94 


3.49 


99.92 


3.93 


99.91 


4.36 


99.88 


_4.8^ 


100 

s 

a 

.2 
Q 


T 
.1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


88 1 


)eg. 


871 Deg. 


8^ Deg. 


87^ Deg. 



TKAVEKSE TABLE. 



c 
% 

3 
? 

1 


3Deg. 


3i Deg. 


3^ 

Lat. 


Deg. 
Dep. 


j 31 Deg. 


f 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


1.00 


0.05 


1. 00 


0.06 


1.00 


0.06 


1.00 


""oToe" 


1 


2 


2.00 


0.10 


2.00 


0.11 


2.00 


0.12 


2.00 


0.13! 2 


3 


3.00 


0.16 


3.00 


0.17 


2.99 


0.18 


2.99 


0.20' 3 


4 


3.99 


0.21 


3.99 


0.23 


3.99 


0.24 


3.99 


0.26' 4 


5 


4.99 


0.26 


4.99 


0.28 


4.99 


0.31 


4.99 


0.33 5 


6 


5.99 


0.31 


5.99 


0.34 


5.99 


0.37 


5.99 


0.39 


fi 


7 


6.99 


0.37 


6.99 


0.40 


6.99 


0.43 


6.99 


0.46 


7 


8 


7.99 


0.42 


7.99- 


0.45 


7.99 


0.49 


7.98 


0.52 


8 


9 


8.99 


0.47 


8.99 


0.51 


8.98 


0..'i5 


8.98 


0.59 


9 


10 
11 


9.99 


0,53 


9.98 


0.57 


9.98 


0.61 


9.98 


0.65 


10 
11 


10.98 


0.58 


10.98 


0.62 


10.98 


0.67 


10.98 


0.72 


13 


11.98 


0.63 


11.98 


0.68 


11.98 


0.73 


11.97 


0.78 


12 


13 


12.98 


0.68 


12.98 


0.73 


12.98 


0.79 


12.97 


0.85 


13 


14 


13.93 


0.73 


13.98 


0.79 


13.97 


0.85 


13.97 


0.92 


14 


15 14.98 


0.79 


14.98 


0.85 


14.97 


0.92 


14.97 


0.98 


15 


16 


15.98 


0.84 


15.97 


0.91 


15.97 


0.98 


15.97 


1.05 


16 


17 


16.98 


0.89 


16.97 


0.90 


16.97 


1.04 


16.96 


1.11 


17 


18 


17.98 


0.94 


17.97 


1.02 


17.97 


1.10 


17.96 


1.18 


18 


19 


18.98 


0.99 


18.97 


1.08 


18.96 


1.16 


18.96 


1.24 


19 


■20 
21 


19.97 


1.05 


19.97 


1.13 


19.96 


1.22 


19.96 


1.31 


20 


20.97 


1. 10 


20.97 


1.19 


20.96 


1.28 


20.96 


1.37 


21 


22 


21.97 


1.15 


21.96 


1.25 


21.96 


1.34 


21.95 


1.44 


22 


23 


22.97 


1.20 


22.96 


1.30 


22.96 


1.40 


22.95 


1..50 


23 


24 


23.97 


1.26 


23.96 


1.36 


23.96 


1.47 


23.95 


1.57 


24 


25 


24.97 


1.31 


24.96 


1.42 


24.95 


1.53 


24.95 


1.64 


25 


26 


25.96 


1.36 


25.96 


1.47 


25.95 


1.59 


25.94 


1.70 


26 


27 


26.96 


1.41 


26.96 


1.53 


26.95 


1.65 


26.94 


1.77 


27 


28 


27.96 


1.47 


27.95 


1.59 


27.95 


1.71 


27.94 


1.83 


28 


29 


28.96 


1.52 


28.95 


1.64 


28.95 


1.77 


28.94 


1.90 


29 


30 
31 


29.96 


1.57 


29 . 95 


1.70 


29.94 


1.83 


29.94 


1.96 
2.03 


30 
31 


30.96 


1.62 


30.95 


1.76 


30.94 


1.89 


30.03 


32 


31.96 


1.67 


31.95 


1.81 


31.94 


1.95 


31.93 


2.09 


32 


33 


33.95 


1.73 


32.95 


1.87 


32.94 


2.01 


32.93 


2.16 


33 


34 


33.95 


1.78 


33.95 


1.93 


33.94 


2.08 


33.93 


2.22 


34 


35 


34.95 


1.83 


34.94 


1.98 


34.93 


2.14 


34.92 


2.29 


35 


36 


35.95 


1.88 


35.94 


2.04 


35.93 


2.20 


35.92 


2.35 


36 


37 


36.95 


1.94 


36.94 


2.10 


36.93 


2.26 


36.92 


2.42 


37 


38 


37.95 


1.99 


37.94 


2.15 


37.93 


2.32 


37.92 


2.49 


38 


39 


.38.95 


2.04 


38.94 


2.21 


38.93 


2.38 


38.92 


2.55 


39 


40 
41 


39.95 


2.09 


39.94 


2.27 


39.93 


2.44 


39.91 


2.62 


40 


40.94 


2.15 


40.93 


2.32 


40.92 


2.. 50 


40.91 


2.68! 41 1 


42 


41.94 


2.20 


41.93 


2.38 


41.92 


2.56 


41.91 


2.75 


42 


43 


42.94 


2.25 


42.93 


2.44 


42.92 


2.63 


42.91 


2.81 


43 


44 


43.94 


2.30 


43.93 


2.49 


43.92 


2.69 


43.91 


2.88 


44 


45 


44.94 


2.36 


4-1.93 


2.55 


44.92 


2.75 


44.90 


2.94 


45 


46 


45.94 


2.41 


45.93 


2.61 


45.91 


2.81 


45.90 


3.01 


46 


47 


46.94 


2.46 


46.92 


2.66 


46.91 


8.87 


46.90 


3.07 


47 


48 


47.93 


2.51 


47.92 


2.72 


47.91 


2.93 


47.90 


3.14 


48 


49 


48.93 


2.56 


48.92 


2.78 


48.91 


2.99 


48.90 


3.20 


49 


50 

" i 

.2 

a 


49.93 


2.62 


49.92 


2.83 


49.91 


3.05 


49.89 


3.27 


_^ 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


J 
.2 

Q 


87'Deg. 


86J Deg. 


86i 


Deg. 


m\ Deg. 



TRAVERSE TABLK. 



[■■ — 


3 Deg. 


3i Deg. 


■y. 


Deg, 


CI Deg. 


C 

B 


1 Lat. 


Dep. 


Lat. 


Dep. 


1 J^at. 


Dep. 


Lat. 


Dep. 


51 


'50.93 


i 2.07 


50.92 


2.89 


: 50.90 


3-11 


"50^89 


3.34 


61 


52 


51.93 


2.72 


51.92 


2.95 


51.90 


3.17 


51.89 


3.40 


52 


53 


52.93 


2.77 


52.91 


3.00 


.52.90 


3.24 


52.89 


3.47 


53 


54 


53.93 


2.83 


.53.91 


3.06 


53.90 


3.30 


53,88 


3.53 


54 


55 


54.92 


2. 88 


54.91 


3.12 


54.90 


3.36 


54.88 


3.60 


55 


56 


55 . 92 


2.93 


55.91 


3.17 


155.90 


3.42 


55.88 


3.66 


50 


57 


56.92 


2.98 


66.91 


3.23 


56.89 


3.48 


.56.88 


3 73 


57 


58 


57.92 


3.04 


57.91 


3.29 


57.89 


3.54 


57.88 


3.79 


58 


59 58.92 


3.09 


58.91 


3.34 


58.89 


3.60 


58.87 


3.86 


59 


60 59.92 


3.14 


59.90 


3.40 


59.89 


3.66 


59.87 


3.92 


60 


61 ,6U.92 


3.19 


60.90 


3.46 


60.89 


3.72 


60.87 


3.99 


61 


62 


61.92 


3.24 


61.90 


.3.51 
3.57 


161.88 


3,79 


61.87 


4.05 


62 


63 


62.91 


3.30 


62.90 


[62.88 


3.85 


62,87 


4.12 


63 


64 


63.91 


3.35:; 63.90 


3.63 


63.88 


3.91 


63.86 


4.19 


64 


65 


64.91 


3.40 1 64.90 


3.69 


64.88 


3.97 


64. S6 


4.25 


65 


60 


65.91 


3.45 


65.89 


3.74 


65.88 


4.03 


65.86 


4.32 


66 


07 


66.91 


3.51 


66.89 


3.80 


66.88 


4>09 


66.86 


4.38 


67 


68 


67.91 


3.56 


67.89 


3.86 


67.87 


4.15 


67.85 


4.45 


68 


69 


68.91 


3.61 


68.89 


3.91 


68.87 


4.21 


68.85 


4.51 


69 


70 
71 


69.90 


3.66 ij 69.89 
3.72 i! 70.89 


3.97 


69.87 


4.27 
4.33 


69.85 
70.85 


4.58 


70 
71 


70.90 


4.03 


70.87 


4.64 


72 


71.90 


3.77 


71.88 


4.08 


71.87 


4.40 


71.85 


,4.71 


72 


73 


72.90 


3.82 


72.88 


4.14 


72.86 


4.46 


72.84 


4.77 


73 


74 


73.90 


3.87 


73.88 


4.20 


73,86 


4.52 


73.84 


4.84 


74 


75 


74 . 90 


3.93 


74.88 


4.25 


74.86 


4,58 


74,84 


4.91 


75 


7n 


75.90 


3.98 


75.88 


4.31 


75.86 


4.64 


75,84 


4.97 


76 


77 


76.89 


4.03 


76.88 


4.37 


76.86 


4,70 


76.84 


5.04 


77 


78 


77.89 


4.08 


77.87 


4.42 


77.85 


4.76 


77,83 


5.10 


78 


79 


78.89 


4.13 


78.87 


4.48 


78.85 


4.82 


78,83 


5.17 


79 


80 
81 


79.89 
80.89 


4.19 
4.24 


79,87 


4.54 


79.85 


4.88 


79,83 


5.23 


80 
81 


80.87 


4.. 59 


80.85 


4.94 


80,83 


5.30 


82 


81.89 


4.29 


81.87 


4.65 


81.85 


5.01 


81,82 


5.36 


82 


83 


82.89 


4.34 


82.87 


4.71 


82,85 


5,07 


82,82 


5.43 


83 


84 


83.88 


4.40 


83.86 


4.76 


83.84 


5,13 


83.82 


5.49 


84 


85 


84.88 


4.45 


84.86 


4.82 


84.84 


5.19 


84.82 


5.56 


85 


86 


85.88 


4.50 


85.86 


4-88 


85,84 


5,25 


85.82 


5.62 


86 


87 


86.88 


4.55 


86.86 


4.93 


86.84 


5,31 


86.81 


5.69 


87 


88 


87.88 


4.61 


87.86 


4.99 


87.84 


5,37 


87.81 


5.76 


88 


89 


88.88 


4.66 


88.86 


5,05 


88.83 


5.43 


88.81 


5.82 


89 


90 
91 


89.88 


4.71 


89.86 


5.10 


89.83 
90.83 


5.49 


89.81 


5.89 


90 
"9T 


90.88 


4.76 


90.85 


5.16 


5.56 


90.81 


5 . 95 


92 


91.87 


4.81 


91.85 


5.22 


91.83 


5.62 


91.80 


6.02 


92 


93 


92.87 


4.87 


92.85 


5.27 


92.83 


5.68 


92.80 


6.08 


93 


94 


93.87 


4.92 


93.85 


5.33 


93.82 


5.74 


93.80 


6.15 


94 


95 


94.87 


4.97 


94.85 


5.39 


94.82 


5.80 


94.80 


6.21 


95 


96 


95.87 


5.02 


95.85 


5.44 


95.82 


5.86 


95.79 


6.28 


96 


97 


96.87 


5.08 


96.84 


5.50 


96.82 


5.92 


96.79 


6., ^4 


97 


98 


97.87 


5.13 


97.84 


5.56 


97.82 


5.98 


97.79 


6.41 


98 


99 


98.86 


5.18 


98.84 


5.61 


98.82 


6.04 


98.79 


6.47 


99 


100 

8 

s 
a 


99.86 


5.23 


99.84 


5.67 


99,81 


6.10 


99.79 


6.54 


100 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dop. 


Lat. 


1 


87 1 


)eg. 


861 Deg. 


SGi 


Deg. 


86i 


Deg. 



10 



TRAVERSE TABLE. 



1 


4 Deg. 


4iDeg. 


H Deg. 


41 Deg. 


9 
1 


Lat. 


Dep. 


Lat. 


Dep.. 




Lat, 


Dep. 


Lat. 


Dep. 


~^l 


1.00 


0.07 


1.00 


0.07 


1.00 


0.08 


1.00 


0.08 


2 2.00 


0.14 


1.99 


0.15 


1.99 


0.16 


1.99 


0.17 




3 2.99 


0.21 


2.99 


0.22 1 


2.99* 


0.24 


2.99 


0.25 


.3 


4 3.99 


0.28 


3.99 


0.30 1 


3.99 


0.31 


3.98 


0.33 


4 


5 4.99 


0.35 


4.99 


0.37 1 


4.98 


0.39 


4.98 


0.41 


5 


6 5.99 


0.42 


5.98 


0.44 


5.98 


0.47 


5.98 


0.50 


6 


7 


6.98 


0.49 


8.98 


0.52 


6.98 


0..55 


6.97 


0.58 


7 


8 


7.98 


0.56 


7.98 


0.59 


7.98 


0.63 


7.97 


0.06 


8 


9 , 


8.98 


0.63 


8.98 


0.67 


8.97 


0.71 


8.97 


0.75 


9 


10 
11 


9.98 


0.70 


9.97 


0.74 


9.97 


0.73 
0.86 


9,97 


0.83 


10 
11 


10.97 


0.77 


10.97 


0.82 


10.97 


10,96 


0.91 


12 


11.97 


0.84 


11.97 


0.89 


11. qe 
12.96 


0.94 


11,96 


0.99 


12 


13 


12.97 


0.91 


12.96 


0.96 


1.02 


12.96 


1.08 


J3 


14 


13.97 


0,98 


13.96 


1.C4 


13.96 


1.10 


13.95 


1.16 


14 


15 


14.96 


1.05 


14.96 


1.11 


14.95 


1.18 


14.95 


1.24 


15 


16 


15.96 


1.12 


15.96 


1.19 


15.95 


1.26 


15.95 


1.32 


16 


17 


16.96 


1.19 


16.95 


1.26 


16.95 


1.33 


16.94 


1.41 


17 


18 


17.96 


1.26 


17.95 


1.33 


17.94 


1.41 


17.94 


1.49 


18 


19 


18.95 


1.33 


18.95 


1.40 


18.94 


1.49 


18.93 


1..57 


19 


20 
21 


19.95 


1.40 


19.95 


1.48 
1.56 


19.94 


1.57 


19.93 


1.66 


20 
21 


20.95 


1.46 


20.94 


20.94 


1.65 


20.93 


1.74 


22 


21.95 


1.53 


21.94 


1.63 


21.93 


1.73 


21.92 


1.82 


22 


23 


22.94 


1.60 


22.94 


1.70 


22.93 


1.80 


22.92 


1.90 


23 


24 


23.94 


1.67' 


23.93 


1.78 


23.93 


1.88 


23.92 


1.99 


24 


25 


24.94 


1.74 


24.93 


1.85 


24.92 


1.96 


24.91 


2.07 


25 


26 


25.94 


1.81 


25.93 


1.93 


25.92 


2.04 


26.91 


2,15 


26 


27 


26.93 


1.88 


26 . 93 


2.00 


26.92 


2.12 


26.91 


2,24 


27 


28 


27.93 


1.95 


27.92 


2.08 


27.91 


2.20 


27.90 


2,32 


28 


29 


28.93 


2.02 


28.92 


2.15 


28.91 


2.28 


28.90 


2,40 


29 


30 
31 


29.93 


2.09 


29.92 


2.22 
"2730 


29.91 


2.35 


29.90 


2.48 


30 
31 


30.92 


2.16 


30.91 


30.90 


2.43 


'30.89 


2.57 


32 


31.92 


2.23 


31.91 


2.37 


31.90 


2.51 


31.89 


2.65 


32 


33 


32.92 


2.30 


32.91 


2.45 


32.90 


2.59 


32.89 


2.73 


33 


34 


33.92 


2.37 


33.91 


2.52 


33.90 


2.67 


33.88 


2.82 


34 


35 


34.91 


2.44 


34.90 


2.59 


34.89 


2.75 


34.88 


2.90 


35 


36 


35.91 


2.51 


35.90 


2.67 


35.89 


2.82 


35.88 


2.98 


36 


37 


36.91 


2.58 


36.90 


2.74 


38.89 


2.90 


36.87 


3.06 


37 


38 


37.91 


2.65 


37.90 


2.82 


37.88 


2.98 


37.87 


3.15 


38 


39 


38.90 


2.72 


38.89 


2.89 


38.88 


3.06 


38.87 


3.23 


39 


40 
41 


39.90 
40.90 


i 2.79 


39.89 


2.96 


39.88 


3.14 


39.86 


3.31 


40 
41 


1 2.86 


40.89 


3.04 


40.87 


3.22 


40.86 


3.40 


42 


41.90 


1 2.93 


41.88 


3.11 


41.87 


3.30 


41.86 


3.48 


42 


43 


42.90 


3.00 


42.88 


3.19 


42.87 


3.27 


42.85 


3.56 


43 


44 


43.89 


': 3.07 


43.88 


3.26 


43.86 


3.45 


43.85 


3.64 


44 


45 


44.89 


3.14 


44.88 


3.33 


44.86 


3.53 


44.85 


3.73 


45 


46 


45.89 


3.21 


45.87 


3.41 


45.86 


3.61 


45.84 


3.81 


46 


47 


46.89 


3.28 


46.87 


3.48 


46.86 


3.69 


46.84 


3.89 


47 


48 


47.88 


3.35 


47,87 


3.56 


47.85 


3.77 


47.84 


3.97 


48 


49 


48.88 


8.42 


48.87 


3.63 


48.85 


3.84 


48.83 


4.06 


49 


_50 

1 




49.88 


3.49^ 


49.86 


3,71 


49.85 


3.92 


49.83 


4.14 


J>0 

c 

i 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 Lat. 


Dep. 


Lat. 


86 


Deg. 


85i Deg, 


85i Deg. 


85i Deg. 



TRAVERSE TABLE. 



11 



5 

n 


4 Dog. 


4i Deg. 


^Deg. 


4| Deg. 


s 
? 
51 


Lat. 


Dep. 


Lat. 

1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


50.88 


3.56 


150.86 


3.78 


50.84 


4.00 


50.82 


4.22 


52 


51.87 


3.63 :\ 51.86 


.3.85 


51.84 


4.08 


51.82 


4.31 


52 


53 


52.87 


3.70 1 52.85 


3.93 


52.84 


4.16 


52.82 


4.39 


53 


54 


53.87 


3.77 11 .53.85 


4.00 


53.83 


4.24 


53.81 


4.47 


54 


55 


54.87 


3.84 , 54.85 


4.08 


54.83 


4.32 


54.81 1 4. 55 


55 


56 


55.86 


3.91 , 55.85! 4.15 


.55.83 


4.39 


55.81 4.64 


56 


57 


56.86 


3.98 i 56.84 


4.22 


56.82 


4.47 


56.80 1 4.72 


57 


58 


57.86 


4.05: 57.84 


4.30 


57.82 


4.55 


57.80 4.80 


58 


59 


58.86 


4.12 :[ 58.84 


4.37 


58.82 


4.63 


58.80 4.89 


59 


60 
61 


59.85 


4.19 
4.26 


59.84 


4.45 


59.82 


4.71 


59.79 4.97 
60.79, 5.05 


60 
61 


60.85 


60.83 


4.. 52 


60.81 


4.79 


62 


61.85 


4.32 i; 61.83 


4.59 


61.81 


4.86 


61.79 


5.13 


62 


63 


62.85 


4.39 ii 62.83 


4.67 


62.81 


4.94 


62.78 


5.22 


63 


64 


63.84 


4.46 1 63.82 


4.74 


63.80 


5.02 


63.78 


5.30 


64 


65 


64.84 


4.53 1 64.82 


4.82 


64.80 


5.10 


64.78 


5.38 


65 


66 


65.84 


4.60 65.82 


4.89 


65.80 


5.18 


65.77 


5.47 


66 


67 


66.84 


4.67 1 66.82 


4.97 


66.79 


5.26 


66.77 


5.55 


67 


68 


67.83 


4.74 67.81 


5.04 


07.79 


5.34 


67.77 


5.63 


68 


69 


68. S3 


4.81 i 68.81 


5.11 


68.79 


5.41 


68.76 


5.71 


69 


70 
71 


69.83 
70.83 


4.88 69.81 


5.19 


69.78 


5.49 


69.76 


5.80 


70 
71 


4.95 1! 70.80 


5.26 


70.78 


5.57 


70 . 76 


5.88 


72 


71.82 


5.02 1; 71.80 


5.34 


71.78 


5.65 


71.75 


5.96 


72 


73 


72.82 


5.09 72.80 


5.41 


72.77 


5.73 


72.75 


6.04 


73 


74 


73.82 


5.16 1,73.80 


■ 5.48 


73.77 


5.81 


73.75 


6.13 


74 


75 


74.82 


5.23 


74.79 


5.56 


74.77 


5.88 


74.74 


6.21 


7.5 


76 


75.81 


5.30 


75.79 


5.63 


75.77 


5.96 


75.74 


6.29 


76 


77 


76.81 


5.37 


' 76.79 


5.71 


76.76 


6.04 


76.74; 6.38 


77 


78 


77.81 


5.44 


77.79 


5.78 


77.76 


6.12 


77.73 


6.46 


78 


79 


78.81 


5.51 


178.78 


5.85 


78.76 


6.20 


78.73 


6.54 


79 


80 
81 


79.81 


5.58 


(79.78 
! 80.78 


5.93 


79.75 


6.28 


79.73 


6.62 


SO 
Si 


80.80 


5.65 


6.00 


80.75 


6.36 


80.72 


6.71 


82 


81.80 


5.72 


181.78 


6.08 


81.75 


6.43 


81.72 


6.79 


82 


83 


82.80 


5.79 


: 82.77 


6.15 


82.74 


6.51 


82.71 


6.87 


83 


84 


83.80 


5.86 


83.77 


6.23 


83.74 


6.59 


83.71 


6.96 


84 


85 


84.79 


5.93 


84.77 


6.30 


84.74 


6.67 


84.71 


7.04 


85 


86 


85.79 


6.00 


85.76 


6.37 


85.73 


6.75 


85.70 


7.12 


86 


87 


86.79 


6.07 


86.76 


6.45 


85.73 


6.83 


86.70 


7.20 


87 


88 


87.79 


6.14 


87.76 


6.52 


87.73 


6.90 


87.70 


7.29 


88 


89 


88.78 


6.21 


88.76 


6.60 


88.73 


6.98 


88.70 


7.37 


89 


90 
91 


89.78 


6.28 


89.75 i 6.67 i 
90.75 1 6.74 


89.72 


7.06 


89.69 


7.45 


90 
91 


90.78 


6.35 


90.72 


7.14 


90.69 


7.54 


92 


91.78 


6.42 91.75 1 6.82 1 


91.72 


7.22 


91.68 


7.62 


92 


93 


92.77 


6.49 


92.74 6.89 


92.71 


7.30 


92.68 


7.70 


93 


94 


93.77 


6.56 


93.74 6.97 


93.71 


7.38 


93.68 


7.78 


94 


95 


94.77 


6.63 


94.74 7.04 


94.71 


7.45 


94.67 


7.87 


95 


96 


95.77 


6.70 95.74 1 7.11 i 


95 . 70 


7.53 


95.67 


7.95 


96 


97 


96.76 


6.77 


96.73, 7.19 


96.70 


7.61 


96.67 


8.03 


97 


98 


97.76 


6.84 


97.73 1 7.26 


97.70 


7.69 


97.66 


8.12 


98 


99 


98.76 


6.91 


98.73 7.34 


98.69 


7.77 


98.66 


8.20 


99 


100 
1 


99.76 


6.98 


99.73: 7.41 


99.69 


7.85 


99.66 


8.28 


100 


Dep. 
86 1 


Lat. 


Dep. Lat. 


Dep. 

851 ] 


Lat. 


Dep. 


Lat. 


1 


fisi 


Deg. 


Oeg. 


85^ Deg. 



12 



TRAVERSE TABLE. 





5 Deg. 


5i Deg. 


5-1 Deg. 


5JDeg. j 


r 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


S 


I 


1.00 


0709" 


1.00 


0.09 


1.00 


0.10 


0.99 


0.10 1 


2 


1.99 


0.17 


1.99 


0,18 


1.99 


0.19 


1.99 


0.20 2 


3 


2.99 


0.26 


2.99 


0.27 


2.99 


0.29 


2.98 


0.30 3 


4 3.98 


0.35 


3.98 


0.37 


3.98 


0.38 


3.98 


0.40 


4 


5 


4.98 


0.44 


4.98 


0.46 


4.98 


0.48 


4.97 


0.50 


f. 


6 


5.98 


0.52 


5.97 


0.55 


5.97 


0.58 


5.97 


0.60 


6 


7 


6.97 


0.61 


0.97 


0.64 


6.97 


0.67 


6.96 


0.70 


7 


8 


7.97 


0.70 


7.97 


0.73 


7.06 


0.76 


7.96 


0.80 


8 


9 


8.97 


0.78 


8.96 


0.82 


8 96 


0.86 


8.95 


0.90 


9 


10 


9.96 


0.87 


9.96 


0.92 


9.95 


0.96 


9.95 


1.00 


Ji 


11 


10.96 


0.96 


10.95 


1.01 


10.95 


1.05 


10.94 


1.10 


111 


12 


11 . 95 


1.05 


11.95 


1.10 


11.94 


1.15 


11.94 


1.20 


12 .; 


13 


12.95 


1.13 


12.95 


1.19 


12.94 


1.25 


12.93 


1.30 


13, 


14 


13.95 


1.22 


13.94 


1.28 


13.94 


1.34 


13.93 


1.40 


14; 


15 


14.94 


1.31 ! 


14.94 


1.37 


14.93 


1.44 


14.92 


1..50 


15 i 


16 15.94 


1.39 1 


15.93 


1.46 


15.93 


1.53 


15.92 


1.60 


16 


17 


16.94 


1.48 1 


16.93 


1.56 


16.92 


1.63 


16.91 


1.70 


17 


13 


17.93 


1..57i 


17.92 


1.65 


17.92 


1.73 


17.91 


1.80 


18 


19 


18.93 


1.66 1 


18.92 


1.74 


18.91 


1.82 


18.90 


1.90 


19 


20 


19.92 


1.74! 
~lT83"; 


19.92 


1.83 


19.91 


1.92 


19.90 
20.89 


2.00 


20 
2\ 


21 


20.93 


20.91 


1.92 


20.90 


"STOT 


2.10 


22 


21.92 


1.92: 


21.91 


2.01 


21.90 


2.11 


21.89 


2.20 


22 


23 


22.91 


2.00 


22.90 


2.10 


22.89 


2.20 


22.88 


2.30 


23 


24 


23.91 


2.09 


23 . 90 


2.20 


23.89. 


2.30 1 


23.88 


2.40 


24 


25 


24.90 


2.18 


24.90 


2.29 


24.88 


2.40 


24.87 


2.50 


25 


26 


25.90 


2.27 


25.89 


2.38 


25.88 


2.49 


25.87 


2.60 


26 


27 


20. 90 


2.35 


26.89 


2.47 


26.88 


2.59 


26.86 


2.71 


27 


28 


27.89 


2.44 


27.88 


2.56 


27.87 


2.68 


27.86 


2.81 


28 


29 


28.89 


2.53 


28.88 


2.65 


28.87 


2.78 


28.85 


2.91 


29 


30 
31 


29.89 


2.61 


29.87 


2.75 
" 2.84 


29.86 


2.88 


29.85 


3.01 


30 


30.88 


2.70 


30.87 


30.86 


2.97 


30.84 


3.11 


31 


32 


31.88 


2.79 


31.87 


2.93 


31.85 


3.07 


31.84 


3.21 


32 


33 


32.87 


2.88 


32.86 


3.02 


32.85 


3.16 


32.83 


3.31 


33 


34 


33.87 


2.9C 


33.86 


3.11 


33.84 


3.26 


33.83 


3.41 


34 


35 


34.87 


3.05 


34.85 


3.20 


34.84 


3.35 


34.82 


3.51 


35 


36 


35.86 


3.14 


35 . 85 


3.29 


35.83 


3.45 


35.83 


3.61 


36 


37 


36.86 


3.22 


36.84 


3.39 


36.83 


3.55 


36.81 


3.71 


37 


38 


37.86 


3.31 


37.84 


3.48 


37.83 


3.64 


37.81 


3.81 


38 


39 


38.85 


3.40 


38.84 


3.57 


.38.82 


3.74 


38.80 


3.91 


39 


40 


39.85 
40.84 


3.49 
3.57 


39.83 


3.66 


39.82 


3.83 
3.93 


39.80 


4.01 


40 
41 


40.83 


3.75 


40.81 


40.79 


4.11 


42 


41.84 


3.66 


41.82 


3.84 


41.81 


4.03 


41.79 


4.21 


42 


43 


42.84 


3.75 


42.82 


3.93 


42.80 


4.12 


42.78 


4.31 


43 


44 


43.83 


3.83 


43.82 


4.03 


43.80 


4.22 


43.78 


4.41 


44 


45 


44.83 


3.92 


44.81 


4.12 


44.79 


4.31 


44.77 


4.51 


45 


46 


45.82 


4.01 


45.81 


4.21 


45.79 


4.41 


45.77 


4.61 


46 


47 


46.82 


4.10 


46.80 


4.30 


46.78 


4.. 50 


46.76 


4.71 


47 


48 


47.82 


4.18 


47.80 


4.39 


47.78 


4.60 


47.76 


4.81 


48 


49 


48.81 


1 4.27 


48,79 


4.48 


48.77 


4.70 


48.75 


4.91 


49 


50 


49.81 


I 4.36 


49.79_ 


4.58 


49.77 


4.79 


49.75 


JAL 


_50 




Dep. 


', Lat. 


Dep. 


Lat. 


Dep. 


Lat, 


Dep. 


Lat. 


1 

s 


85 


Deg. 


841 


De,ir. 


m 


Deg 


84^ 


Deg. 



TRAVKIiSK TABLl- 



13 



51 


5 Deg. 


5i Deg. 


H 


Deg. 


Lat. 


Deg-. 


C 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


DepT; i 
5."lT 61 


50.81 


4.44 


50.79 


4.67 


50.77 


4.89 


50.74 


52 


51.80 


4.53 


51.78 


4.76 


51.76 


4.98 


51.74 


5.21 52 


53 


52.80 


4.62 


52.78 


4.85 


52.76 


5.08 


62.73 


5.31 5,. 


54 


53.79 


4,71 


53.77 


4.94 


53.75 


5.18 


.53.73 


5.41 5; 


65 


.'■>1.V9 


4.79 


54.77 


5.03 


54.75 


5.27 


.54.72 


5.51 i 5:. 


56 


55.79 


4.88 


55.77 


5.12 


55.74 


5.37 


.55.72 


5.61 i 5ii 


57 


56.78 


4.97 


56.76 


5.22 


56.74 


5.46 


5«.71 


5.71 57 


58 


57.78 


5.06 


57.76 


5.31 


57.73 


5.56 


57.71 


5.81 58 


59 


58.78 


5.14 


.58.75 


5.40 


58.73 


5.65 


58.70 


5.91 59 


60 

61 


59.77 


5.23 


59.75 


5.49 


59.72 
60.72 


5.75 


59.70 


6.01 60 


60.77 


5.32 


60.74 


5.58 


5.86 


60.69 


6.11 


61 


62 


61.76 


5.40 


61.74 


5.67 


61.71 


5.94 


61.69 


6.21 


62 


63 


62.76 


5.49 


62.74 


5.76 


62.71 


6.04 


62.68 


6.31 


63 


64 


63.76 


5.58 


63.73 


5.86 


63.71 


6.13 


63.68 


6.41 


64 


65 


64.75 


5.67 


64.73 


5.95 


64.70 


6.23 


64.67 


6.51 


65 


66 


65.75 


5.75 


65.72 


6.04 


65.70 


6.33 


65.67 


6.61 


66 


67 


66.75 


5.84 


66.72 


6.13 


66.69 


6.42 


66.66 


6.71 


67 


68 


67.74 


5.93 


67.71 


6.22 


67.69 


6.52 


67.66 


6.81 


68 


69 


68.74 


6.01 


68.71 


6.31 


68.68 


6.61 


68.65 


6.91 


69 


70 

71 


69.73 


6.10 


69.71 


6.41 


69.68 


6.71 


69.65 


7.01 


70 


70.73 


6.19 


toTto" 


6.50 


70.67 


6.81 


70.64 


7.11 


71 


72 


71.73 


6.28 


71.70 


6.59 


71.67 


6.90 


71.64 


7.21 


7-/ 


^3 


72.72 


6.36 


72.69 


6.68 


72.66 


7.00 


72.63 


7.31 


7S 


74 


73.72 


6.45 


73.69 


6.77 


73.66 


7.09 


73.63 


7.41 


74 


75 


74.71 


6.54 


74.69 


6.86 


74.65 


7.19 


74.62 


7.51 


75 


76 


75.71 


6.62 


75.68 


6.95 


75.65 


7.28 


75.62 


7.61 


76 


77 


76.71 


6.71 


76.68 


7.05 


76.65 


7.38 


76.61 


7.71 


77 


78 


77.70 


6.80 


77.67 


7.14 


77.64 


7.48 


77.61 


7.81 


78 


79 


78.70 


6.89 


78.67 


7.23 


78.64 


7.57 


78.60 


7.91 


79 


80 
81 


79.70 
80.69 


6.97 


79.66 


7.32 


79.63 


7.67 


79.60 


8.02 


80 


7.06 


80.66 


7.41 


80.63 


7.76 


80.59 


8.12 


81 


82 


81.69 


7.15 


81.66 


7.50 


81.62 


7.86 


81.59 


8.22 


82 


83 


82.68 


7.23 


82.65 


7.59 


82.62 


7.96 


82.58 


8.32 


83 


84 


83.68 


7.32 


83.65 


7.69 


83.61 


8.05 


83.58 


8.42 


84 


85 


84.68 


7.41 


84.64 


7.78 


84.61 


8.15 


84.. 57 


8.52 


85 


86 


85.67 


7.. 50 


85.64 


7.87 


85.60 


8.24 


85.57 


8.62 


86 


87 


86.67 


7.58 


86.64 


7.96 


86.60 


8.34 


86.. 56 


8.72 


87 


88 


87.67 


7.67 


87.63 


8.05 


87.59 


8.43 


87.56 


8.82 


88 


89 


88.66 


7.76 


88.63 


8.14 


88.59 


8.53 


88.55 


8.92 


89 


90 
91 


89.66 


7.84 


89.62 


8.24 


89.59 


8.63 


89.55 


9.02 


90 


90.65 


7.93 


90.62 


8.33 


90.68 


8.72 


90.54 


9.12 


91 


92 


91.65 


8.02 


91.61 


8.42 


91.58 


8.82 


91.54 


9.22 


92 


93 


92.65 


8.11 


92.61 


8.51 


92.57 


8.91 


92.53 


9.32 


93 


94 


93.64 


8.19 


93.61 


8.60 


93.57 


9.01 


93.53 


9.42 


94 


95 


94.64 


8.28 


94.60 


8.69 


94.56 


9.11 


94.52 


9.52 


95 


96 


95.63 


8.37 


95.60 


8.78 


95.56 


9.20 


95.52 


9.62 


96 


97 


96.63 


8.45 


96.59 


8.88 


96.55 


9.30 


96.51 


9.72 


97 


98 


97.63 


8.54 


97.59 


8.97 


97.55 


9.39 


97.51 


9.82 


98 


99 


98.62 


8.63 


98.59 


9.06 


98.54 


9.49 


98.50 


9.92 


99 


100 

1 

Q 


99.62 


8.72 


99.58 


9.15 


99.54 


9.58 


99.50 


10.02 


100 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


J 


85 1 


)eg. 


84iDeg. 


84i 


Deg. 


84i Deg. 



20 



14 



TRAVERSE TABLE. 





6D 


... 


64 Deg. 


6iDeg. 


H Deg. 


O 

3 
P 

1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


~T 


0.99 


0.10 


0.99 


0.11 


0.99 


0.11 


0.99 


0.12 


2 


1.99 


0.21 


1.99 


0.22! 


1.99 


0.23 


1.99 


0.24 


2 


3 


2.98 


0.31 


2.98 


0.33 


2.98 


0.34 


2.98 


0.35 


3 


4 


3.98 


0.41 


3.98 


0.44 


3.97 


0.45 


3.97 


0.47 


4 


5 


4.97 


0.52 


4.97 


0.54 


4.97 


0.57 


4.97 


0.59 


5 


6 


5.97 


0.63 


5.96 


0.65 


5.96 


0.68 


5.96 


0.71 


6 


7 


6.96 


0.73 


6.96 


0.76 


6.96 


0.79 


6.95 


0.82 


7 


8 


7.96 


0.84 


7.95 


0.87 


7.95 


0.91 


7.94 


0.94 


8 


y 


8.95 


0.94 


8.95 


0.98 


8.94 


1.02 


8.94 


1.06 


9 


10 

11 


9.95 
10.94 


1.05 


9.94 


1.09 


9.94 


1.13 
1.25 


9.93 


1,18 
1.29 


10 
11 


1.15 


10.93 


1.20 


10.93 


10.92 


12 


11.93 


1.25 


11.93 


1.31 


11.92 


1.36 


11.92 


1.4J 12 


13 


12.93 


1.36 


12.92 


1.42 


12.92 


1.47 


12.91 


1..53 13 


14 


13.92 


1.46 


13.92 


1.52 


13.91 


1.59 


13.90 


1.65 14 


15 


14.92 


1.57 


14.91 


1.63 


14.90 


1.70 


14.90 


1.76 15 


16 


15.91 


1.67 


15.90 


1.74 


15.90 


1.81 


15.89 


1.88' 16 


17 


16.91 


1.78 


16.90 


1.85 


16.89 


1.92 


16.88 


2 00 i 17 


18 


17.90 


1.88 


17.89 


1.96 


17.88 


2.04 


17.88 


2.12 1 18 


19 


18.90 


1.99 


18.89 


2.07 


18.88 


2.15 


18.87 


2.23 i 19 


20 


19.89 


2.09 


19.88 


2.18 


19.87 


2.26 


19.86 


2.35! 20 


21 


20,88 


2.20 


20.88 


2.29 


20.87 


2.38 


20.85 


2.47 


21 


22 


21.83 


2.30 


21.87 


2.40 


21.86 


2.49 


21.85 


2.59 


22 


23 


22.87 


2.40 


22.86 


2.50 


22.85 


2.60 


22.84 


2.70 


23 


24 


23.87 


2.51 


23.86 


2.61 


23.85 


2.72 


23.83 


2.82 


24 


25 


24.86 


2.61 


24.85 


2.72 


24.84 


2.83 


24.83 


2.94 


25 


26 


25.86 


2.72 


25.85 


2.83 


25.83 


2.94 


25.82 


3.06 


26 


27 


26.85 


2.82 


26.84 


2.94 


26.83 


3.06 


26.81 


3.17 


27 


28 


27.85 


2.93 


27.83 


3.05 


27.82 


3.17 


27.81 


3.29 


28 


29 


28.84 


3.03 


28.83 


3.16 


28.81 


3.28 


28.80 


3.41 


29 


30 
'31 


29.84 


3.14 


29.82 


3.27 


29.81 


3.40 


29.79 


3.. 53 


30 


30.83 


3.24 


30.82 


3.37 


30.80 


3.51 


30.79 


3.64 1 31 1 


32 


31 82 


3.34 


31.81 


3.48 


31.79 


3.62 


31.78 


3.76 


32 


33 


32.82 


3.45 


32.80 


3.59 


32.79 


3.74 


32.77 


3.88 


33 


34 


.33.81 


3.55 


33.80 


3.70 


33.78 


3.85 


33.76 


4.00 


34 


35 


34.81 


3.66 


34.79 


3.81 


34.78 


3.96 


34.76 


4.11 


35 


36 


35.80 


3.76 


35.79 


3.92 


35.77 


4.08 


35.75 


4.23 


36 


37 


36.80 


3.87 


36 . 78 


4.03 


36.76 


4.19 


36.75 


4.35 


37 


38 


37.79 


3.97 


37.77 


4.14 


37 . 76 


4.30 


37.74 


4.47 


38 




38.79 


4.08 


38.77 


4.25 


38.75 


4.41 


38.73 


4.. 58 


39 


40 


39.78 


4.18 


39.76 


4.35 


39.74 


4.53 


39,72 


4.70 
4.82 


40 
41 


41 


40.78 


4.29 


40.76 


4.46 


40.74 


4.64 


40.72 


42 


41.77 


4.39 


41.73 


4.57 


41.73 


4.76 


41.71 


4.94 


42 


43 


42.76 


4.49 


42.74 


4.68 


42.72 


4.87 


42.70 


5.05 i 43 


44 


43.76 


4.60 


43.74 


4.79 


43.72 


4.98 


43.70 


5.17, 44 


45 


44.75 


4.70 


44.73 


4.90 


44.71 


5.09 


44.69 


5.29 45 


46 


45.75 


4.81 


45.73 


5.01 


45.70 


5.21 


45.68 


5.41 1 46 


47 


46.74 


4.91 


46 . 72 


5.12 


46.70 


5.32 


46.67 


5.52 


47 


48 


47.74 


5.02 


47.71 


5.23 


47.69 


5.43 


47.67 


5.64 


48 


49 


48.73 


5.12 


48.71 


6.34 


48.69 


5.55 


48.06 


5.76 


49 


50 


49.73 


5.23 


49.70 


5.44 


49.68 


5.66 


49.65 


5.88 


_50^ 


■s 


Dop. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


1 






" 






Q 


84 


Deg. 


83.1 


Deg. 


831 


Deg. 


83i Deg.- 


5 











TRAVERSE 


TABLK. 






15 






1 
~51 


6Deg. 


6i Deg. 


61 Deg 


61 Deg. 


p 
I 

51 






Lat. 


Dep. 


Lat. 


Dep. 


Lat 
50.67 


Dep. 


Lat. 


Dep. 






50.72 


5.33 


50.70 


5.55 


5.77 


50.65 


5.99 






52 51.72 


5.44 


51.69 


5.66 


51.67 


5.89 


51.64 


6.11 


52 






53 52.71 


5.. 54 


52.68 


5.77 


.52.66 


6.00 


52.63 


6,23 


53 






51 .53.70 


5.64 


\53.68 


5.88 


53.65 


6.11 


53.63 


6.35 


54 






5:5 .54.70 


5.75 


54.67 


5.99 


54.65 


6.23 


54.62 


6.46 


55 






56 .55.69 


5.85 


55.67 


6.10 


55.64 


6.34 1 


55.61 


6.58 


56 






57; 56.69 


5.96 


56.66 


6.21 


56.63 


6.45 


56.60 


6.70 


57 






58 ! 57.68 


6.06 


57.66 


6.31 


57.63 


6.57 


67.60 


6.82 


58 






59 58.68 


6.17 


58.65 


6.42 


.58.62 


6-68 


58.59 


6.93 


59 






_fiO 


59.67 


6.27 


59.64 


6.53 


59.61 


6.79! 


59.. 58 


7.05 


60 
"61 






61 


60.67 


6.. 38 


60.64 


6.64 


50.61 


6.91I 


60.58 


7.17 






62 


61.66 


6.48 


61.63 


6.75 


61.60 


7.02 


61.57 


7.29 


62 






63 


62.65 


6.59 


62.63 


6.86 


62.60 


7.13! 


62.. 56 


7.40 


63 






64 


63.65 


6.69 


63.62 


6.97 


63.59 


7.25, 


63.56 


7.52 


64 






65 


64.64 


6.79 


64.61 


7.08 


64.58 


7.36 


64.55 


7.64 


65 






66 


65.64 


6.90 


65.61 


7.19 


65.58 


7.47 1 


65.54 


7.76 


66 






67 


66.63 7.00 


66.60 


7.29 


66.57 


7 58 


66.54 


7.88 


67 






68 


67.63 7.11 


67.60 


7.40 


67.56 


7.70 


67.53 


7.99 


68 






69 


68 . 62 


7.21 


68 . 59 


7.51 


68.56 


7.81 


68.52 


8.11 


69 






70 


69.62 


7.32 


69.58 


7.62 


69.55 


7.92 


69.51 


8.23 


70 
71 




"71 


70.61 


7.42 


70.58 


7.73 


70.54 


8.04 


70.51 


8.. 35 






72 


71.61 


7.53 


71., 57 


7.84 


71.. 54 


8.15 


71.50 


8.46 


72 






73 


72.60 


7.63 


72.57 


7.95 


72.. 53 


8.26 


72.49 


8.58 


73 






74 


73.. 59 


7.74 


73.50 


8.06 


73.. 52 


8.38 


73.49 


8.70 


74 






75 


74.59 


7.84 


74.55 


8.17 


74.52 


8.49 


74.48 


8.82 


75 






76 


75.58 


7.94 


75.. 55 


8.27 


75.51 


8.60 


75.47 


8.93 


76 






77 


76.58 


8.05 


76.54 


8.38 


76.51 


8.72 


76.47 


9.05 


77 






78 


77.57 


8.15 


77.. 54 


8.49 


77.50 


8.83 


77.46 


9.17 


78 






79 


78.. 57 


8.26 


78.53 


8.60 


78.49 


8.94 


78.45 


9.29 


79 






80 
81 


79.56 


8.36 


79.53 


8.71 


79.49 
80.48 


9.06 


79.45 


9.40 


80 
81 






80.56 


8.47 


80.52 


8.82 


-9:17 


80.44 


9.52 






82 


81.. 55 


8.57 


81.51 


8.93 


81.47 


9.28 


81.43 


9.64 


82 






83 


82.55 


8.68 


82.51 


9.04 


82.47 


9.40 


82.42 


9.76 


83 






84 


83.54 


8.78 


83.50 


9.14 


H3.46 


9.51 


83.42 


9.87 


84 






85 


84.53 


8.88 


84.. 50 


9.25 


84.45 


9.62 


84.41 


9.99 


85 






86 


85.53 


8.99 


85.49 


9.36 


85.45 


9.74 


85.40 


10.11 


86 






87 


86.52 


9.09 


86.48 


9.47 


86.44 


9.85 


86.40 


10.23 


87 






88 


87.52 


9.20 


87.48 


9.58 


87.43 


9.96 


87.39 


10.34 


88 






89 


88.51 


9.30 


88.47 


9.69 


88.43 


10.08 


88.38 


10.46 


89 






90 
91 


89.51 


9.41 


89.47 


9.80 


89.42 


10.19 


89.38 


10.58 


90 
91 




90.50 


9.51 


90.46 


9.91 


90.42 


10.30 


90.37 


10.70 






92 


91.50 


9.62 


91.45 


10.02 


91.41 


10.41 


191.30 


10.81 


92 






93 


92.49 


9.72 


92.45 


10.12 


92.40 


10.. 53 


'92.36 


10.93 


93 






94 


93.49 


9.83 


93.44 


10.23 


93.40 


10.64 


193.. 35 


11.05 


94 






95 


94.48 


9.93 


94.44 


10.34 


94.39 


10.75 


: 94.. 34 


11.17 


95 






96 


95.47 


10.03 


95.43 


10.45 


95.38 


10.87 


95.33 


11.28 


96 






97 


96.47 


10.14 


96.42 


10.56 


96.38 


10. 9S 


96.33 


11.40 


97 






98 


97.46 


10.24 


97.42 


10.67 


97.37 


11.09 


97.32 


11.52 


98 






99 


98.46 


10.35 


98.41 


10.78 


98.. 36 


11.21 


98.31 


11.64 


99 






100 


99.45 


10.45 


99.41 


10.89 


99.36 


11.32 


99.31 


11.75 


100 

g 
1 




Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 




















If. 


84 Deg. 


831 


Deg. 


83| 


Deg. 


83i 


Deg. 


a 





16 



TRAVERSE TABLE. 



5 

1 
P 
1 


7Deg. 


7i Deg. 


71 Deg 


71 


Deg, 


1 


Lat. 


Dep. 


Lat. 
0.99 


Dtp. 


Lat. 


Dep. 


Lat. 


Dep. 


0.99 


0.12 


0.13 


0.99 


0.13 


0.99 


0.13 


"Y 


2 


1.99 


0.24 


1.98 


0.25 


1.98 


0.20 


1.98 


0,27 


2 


3 


2.98 


0.37 


2.98 


0.38 


2.97 


0.39 


2.97 


0.40 


3 


4 


3.97 


0.49 


3.97 


0.50 


3.97 


0.52 


3.96 


0,54 


4 


5 


4.96 


0.61 


4.96 


0.63 


4.96 


0.65 


4.95 


0,67 


5 


6 


5.96 


0.73 


5.95 


0.76 


5.95 


0.78 


5.95 


0,81 


6 


7 


6.95 


0.85 


0.94 


0.88 


6.94 


0.91 


6.94 


0,94 


7 


8 


7.94 


0.97 


7.94 


1.01 


7.93 


1.04 


7.93 


1.08 


8 


9 


8.93 


1.10 


8.93 


1.1 1- 


8.92 


1.17 


8.92 


1.21 


9 


10 
11 


9.93 
10.92 


1.22 


9.92 


1.26 


9.91 


1.31 


9.91 


1.35 


10 


1.34 


10.91 


1.39 


10.91 


1.44 


10.90 


1,48 


11 


12 


il.9i 


1.46 


11.90 


1.51 


11.90 


1.57 


11.89 


1,62 


12 


13 


12.90 


1.58 


12.90 


1.64 


12.89 


1.70 


12,88 


1,75 


13 


14 


13.90 


1.71 


13.89 


1.77 


13.88 


1.83 


13.87 


1.89 


14 


15 


14.89 


1.83 


14.88 


1.89 


14.87 


1.96 


14.86 


2.02 


15 


16 


15.88 


1.95 


15.87 


2.02 


15.86 


2.09 


15.85 


2,16 161 


17 


16.87 


2.07 


16.86 


2.15 


16.85 


2.22 


16.84 


2,29 


17 


18 


17.87 


2.19 


17.86 


2.27 


17.85 


2.35 


17.84 


2.43 


18 


19 


18.86 


2.32 


18.85 


2.40 


18.84 


2.48 


18,83 


2.56 


19 


20 
21 


19.85 


2.44 i 


19.84 


2.52 


19.83 


2.61 


19,82 


2.70 


20 

21 


20.84 


2.56 


20.83 


2.65 


20.82 


2.74 


20.81 


2.83 


22 


21.84 


2.68 


21.82 


2.78 


21.81 


2.87 


21,80 


2.97 


22 


23 


22.83 


2.80 


22.82 


2.90 


22.80 


3.00 


22.79 


3.10 


23 


24 


23.82 


2.92 


23.81 


3.03 


23.79 


3.13 


23.78 


3.24 


24 


25 


24.81 


3.05 


24.80 


3.15 


24.79 


3.26 


24,77 


3.37 


25 


26 


25.81 


3.17 


25.79 


3.28 


25.78 


3.39 


25.76 


3.51 


26 


27 


20.80 


3.29 


26.78 


3.41 


26.77 


3.52 


26.75 


3.64 


27 


28 


27.79 


3.41 


27.78 


3.53 


27.76 


3.65 


27.74 


3.78 


28 


29 


28.78 


8.53 


28.77 


3,66 


28.75 


3.79 


28.74 


3.91 


29 


30 


29.78 


3.06 


29.76 


3.79 


29.74 


3.92 


29.73 


4,05 


30 


31 


30.77 


3.78 


30.75 


3.91 


30.73 


4.05 


30.72 


4.18 


31 


32 


31.76 


3.90 


31.74 


4.04 


31.73 


4.18 


31.71 


4,32 


32 


33 


32.75 


4.02 


32.74 


4.16 


32.72 


4.31 


32.70 


4,45 


33 


34 


33.75 


4.14 


33.73 


4.29 


33.71 


4.44 


33.69 


4,58 


34 


35 


34.74 


4.27 


3'1.72 


4.42 


34.70 


4.57 


34.68 


4,72 


35 


36 


35.73 


4.39 


35 .7 1 


4.54 


35 . 69 


4.70 


35.67 


4,85 


36 


37 


36.72 


4.51 


36.70 


4.67 


36 . 68 


4.83 


36.66 


4.99 


37 


38 


37.72 


4.C3 


37.70 


4.80 


37.67 


4.96 


37.65 


5,12 


38 


^ 


38.71 


4.75 


38.69 


4.92 


.38.67 


B.09 


38,64 


5.26 


39 


40 
41 


39.70 
40.70 


4.87 
5.00 


39 . 68 


5.05 


39.66 
40.65 


5.22 


.39,63 


5.39 


40 
41 


40.67 


5.17 


5.35 


40.63 


5.. 53 


42 


41.09 


5.12 


41.66 


5.30 


41.64 


5.48 


41,62 


5.66 


42 


43 


42.68 


5.24 


42.66 


5.43 


42.03 


5.61 


42.61 


5.80 


43 


44 


43.67 


5.30 


43.65 


5.55 


43.62 


5.74 


43.60 


5.93 


44 


45 44.67 


5.48 


44.64 


5.68 


44.62 


5.87 


44.. 59 


6.07 


45 


46 


45 . 66 


5.61 


45.63 


5.81 


45.61 


6.00 


45.58 


6.20 


46 


47 


46.65 


5 . 73 


46.62 


5.93 


46.60 


6.13 


; 46.57 


6.34 


47 


48 


47.64 


5.85 


47.62 


6.06 


47.59 


6.27 


47.. 56 


6.47 


48 


49 


48.63 


5.97 


48.61 


6.18 


48.58 


6.40 


1 48.55 


6.61 


49 


50_ 

c 
Q 


49.63 


6.09 


49.60 


6.31 


49.57 


_6.53^ 


49.54 


6.74 


_50 


Dep, 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


1 
.2 
P 


83 Deg. 


821 Deg. 


821 Deg. 


m Deg. 



Til AVERSE TABLE. 



17 





7Deg. 


n Deg. 


n Deg- 


7$ Deg. 


1 

"51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat, 


Dep. 


Lat. 


Dep. 


50,62 


6.22 


50.59 


6.44 


.50.56 


6.66 


"50:53^ 


6.88 


52 


51. Gl 


6.34 


51.58 


6.56 


51,56 


6,79 


51.53 


7.01 1 .52 1 


53 


52.60 


6.46 


,52.58 


6.69 


,52,55 


6,92 


52.52 


7.15 531 


54 


53.60 


6.58 


53,57 


6.81 


53.54 


7.05 


.53.51 


7.28 


54 


55 


54.59 


6.70 


54,56 


6.94 


54.53 


7.18 


54.50 


7.43 


55 


56 


55.58 


6,82 


55,55 


7,07 


55.52 


7.31 


55.49 


7.55 


56 


57 


56.58 


6.95 


56 , 54 


7.19 


56.51 


7.44 


56.48 


7.69 


57 


58 


57.57 


7.07 


57.54 


7.32 


57.50 


7,57 


57.47 


7.82 


58 


59 


.53.56 


7.19 


58.53 


7.45 


58.50 


7.70 


58.46 


7.96 


59 


60 
61 


59.55 


7.31 


59.52 


7.57 


59.49 


7.83 


59.45 


8.09 


60 


60.55 


7.43 


60.51 


7.70 


60.48 


7,96 


60.44 


8.23 


61 


62 


61.54 


7.56 


61.50 


7.82 


61.47 


8,09 


61.43 


8.3H 


62 


63 


62.. 53 


7.68 


62.50 


7.95 


62.46 


8.22 


62.42 


8.50 


63 


64 


63.52 


7.80 


63.49 


8.08 


63.45 


8.35 


63.42 


8.63 


64 


65 


64.52 


7.92 


64.48 


8,20 


64.44 


8.48 


64.41 


8.77! 65 


66 


65.51 


8.04 


05.47 


8,33 


65.44 


8,61 


65.40 


8.90 1 66 


67 


66 50 


8.17 


66.46 


8.40 


66.43 


8,75 


66.39 


9 . 04 1 67 


68 


67.49 


8.29 


67.46 


8.58 


67.42 


8.88 


67.38 


9. It 


68 


69 


68.49 


8.41 


68.45 


8.71 


68.41 


9,01 


68.37 


9.30 


69 


70 
71 


69.48 


8,53 


69.44 


8.83 


69,40 


9.14 


69.36 


9.44 


70 


70.47 


8,65 


70.43 


8.96 


70.39 


9.27 


70.35 


9.57 


71 


72 


71.46 


8.77 


71,42 


9.09 


71.38 


9.40 


71.34 


9.71 


72 


73 


72.46 


8.90 


72.42 


9.21 


72 38 


9.. 53 


72.33 


9.84 


73 


74 


73.45 


9.02 


73.41 


9.34 


73,37 


9.66 


73.32 


9.98 


74 


75 


74.44 


9.14 


74.40 


9.46 


74,36 


9,79 


74.31 


10,11 


75 


76 


75.43 


9.26 


75.39 


9.59 


75,35 


9.92 


75.31 


10,25 


76 


77 


76.43 


9.38 


I 76.. 38 


9,72 


76.34 


10.05 


76.30 


10,38 


77 


78 


77.42 


9.51 


77.38 


9.84 


77,33 


10.18 


77.29 


10.52 


78 


79 


78.41 


9.63 


78.37 


9.97 


78,32 


10.31 


78.28 


10.65 


79 


80 
81 


79.40 


9.75 


79.36 


10.10 


79.32 
8073T 


10.44 


79.27 


10.79 


80 
81 


80.40 


9.87 


80.35 


10.22 


10.57 


80.26 


10,92 


82 


81.39 


9.99 


81. .34 


10,35 


81.30 


10.70 


81.25 


11.06 


82 


83 


82.38 


10.12 


82,34 


10,47 


82.29 


10.83 


82.24 


11.19 


83 


84 


83.37 


10.24 


83.33 


10.60 


83.28 


10.96 


83.23 


11.33 


84 


85 


84.37 


10.36 


84.32 


10.73 


84.27 


11.09 


84.22 


11.46 


85 


86 


85.36 


10.48 


85.31 


10.85 


85.26 


11.23 


85.21 


11.60 


86 


87 


86.35 


10.60 


86.30 


10.98 


86.26 


11.36 


86.21 


11.73 


87 


88 


87.34 


10.72 


87.30 


11,11 


87.25 


11,49 


87.20 


11.87 


88 


89 


88.34 


10,85 


88.29 


11.23 


88.24 


11.62 


88.19 


12.00 


89 


90 
^1 


89.33 


10 97 


89.28 


11.36 


89.23 


11.75 


89.18 


12.14 


90 


90.32 


11,09 


90.27 


11,48 


90.22 


11.88 


90.17 


12.27 


91 


92 


91.31 


11,21 


91.26 


11.61 


91.21 


12.01 


91.16 


12,41 


92 


93 


92.31 


11.33 


92.26 


11.74 


92.20 


12.14 


92.15 


12.54 


93 


94 


93.30 


11.46 


93.25 


11.86 


93.20 


12.27 


93.14 


12.68 


94 


95 


94.29 


11.58 


94.24 


11.99 


94.19 


12.40 


94.13 


12.81 


95 


96 


95.28 


11.70 


95.23 


12.12 


95.18 


12.53 


95.12 


12.95 1 961 


97 


96.28 


11.82 


96.22 


12.24 


96.17 


12.66 


96.11 


13,08 


97 


98 


97.27 


11.94 


97.22 


12.37 


97,16 


12.79 


97.10 


13.22 


98 


99 


98.26 


12.07 


98.21 


12.49 


98,15 


12,92 


98.10 


13.35 


99 


100 

5 


99.25 


12.19 


99.20 


12.62 


99.14 


13.05 


99.09 


13.49 


100 

1 
.2 
Q 


Dep. 


Lat. 


Dep, 


Lat, 


Dep. 


Lat. 


Dep. 


Lat. 


83 1 


3eg. 


821 


Deg. 


82^ Deg. 


82i Deg. 



18 



TRAVERSE TABLE. 





8 Beg. 


iii Deg. 


8-k Deg. 


8J Deg. 


a 
9 


Lai. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.99 


0.14 


0.99 


0.14 


~o:m' 


0.15 


0.99 


0.15 


~T 


3 


1.98 


0.28 


1.98 


0.29 


1.98 


0.30 


1.98 


0.30 


2 


3 


2.M7 


0.42 


2.97 


0.43 


2.97 


0.44 


2.97 


0.46 


3 


4 


3.9G 


0..56 


3.96 


0.57 


3.96 


0.,59 


3.95 


0.61 


4 


5 


4.95 


0.70 


4.95 


0.72 


4.95 


0.74 


4.94 


0.76 


5 


6 


5.94 


0.84 


5.94 


0.86 


5.93 


0.89 


5.93 


91 


6 


7 


6.93 


0.97 


6.93 


1.00 


6.92 


1.03 


6.92 


1.06' 7 


8 


7.92 


1.11 


7.92 


1.15 


7.91 


1.18 


7.91 


1 22 8 


9 


8.91 


1.25 


8.91 


1.29 


8.90 


1.33 


8.90 


1.37 1 9 


10 


9.90 


1.39 


9.90 


1.43 


9.89 


1.48 


9.88 


1.52 1 10 


M 


10.89 


1.53 


10.89 


1..58 


10.88 


1.63 


10.87 


1.67 11 


12 


J 1.88 


1.67 


11.88 


1.72 


11.87 


1.77 


11.86 


1.83 


12 


13 


12.87 


1.81 


12.87 


1.87 


12.86 


1.92 


12.85 


1.93 


13 


14 


13.86 


1.95 


13.86 


2.01 


13.85 


2.07 


13.84 


2.13 


14 


15 


14.85 


2.09 


14.85 


2.15 


14.84 


2.23 


14.83 


2.28 


15 


16 


15.84 


2.23 


15.84 


2.30 


15.82 


2.36 


15.81 


2.43 


16 


17 


16.83 


2.37 


16.83 


2.44 


16.81 


2.51 


16.80 


2.59 


17 


IS 


"17.82 


2.51 


17.81 


2.58 


17.80 


2.66 


17.79 


2.74 


18 


19 


18.82 


2.64 


18.80 


2.73 


18.79 


2.81 


18.78 


2.89 


19 


20 


19.81 


2.78 


19.79 


2.87 


19.78 


2.96 


19.77 


3.04 


20 
" 21 


21 


20 . 80 


2 . 92 


20.78 


3.01 


20.77 


3.10 


20.76 


3.19 


22 21.79 


3.06 


21.77 


3.16 


21.76 


3.25 


21.74 


3.35 


22 


23 22.78 


3.20 


22.76 


3.30 


22.75 


3.40 


22.73 


3.50 


23 


24 23.77 


3.34 


23.75 


3.44 


23.74 


3.55 


23.72 


3.65 


24 


2.5 24.76 


3.48 


24 . 74 


3.59 


24.73 


3.70 


24.71 


3.80 


25 


20 25.75 


3.62 


25.73 


3.73 


25.71 


3.84 


25.70 


3.96 


26 


27 26.74 


3.76 


26.72 


3.87 ,26.70 


3.99 


26.69 


4.11 


27 


28 27.73 


3.90 


27.71 


4.02 


27.69 


4.14 


27.67 


4.26 


28 


29 1 28 . 72 


4.04 


28.70 


4.16 


28.68 


4.29 


28.66 


4.41 


29 


30 


29.71 


4.18 


29.69 


4.30 
4.45 


29.67 


4.43 


29.65 


4.56 


30 


3Y 


30.70 


4.31 


30.68 


30.66 


4.58 


30.64 


4.72 


31 


32 1 31.69 


4.45 


31.67 


4.59 


31.65 


4.73 


31.63 


4.87 


32 


33 132.68 


4.59 


32.66 


4.74 


32.64 


4.88 


32.62 


5.02 


33 


34 


33.67 


4.73 


33.65 


4.88 


33.63 


5.03 


33.60 


5.17 


34 


35 


34.66 


4.87 


34.64 


5.02 


34.62 


5.17 


34.-59 


5.32 


35 


36 


35.65 


5.01 


35.63 


5.17 


35.60 


5.32 


135.58 


5.48 


36 


37 


36.64 


5.15 


36.62 


5.31 


36.. 59 


5.47 


36.57 


5.63 


37 


38 


37.63 


5.29 


37.61 


5.45 


37.58 


5.62 


37.56 


5.78 


38 


39 


38.62 


5.43 


38.60 


5.60 


38.57 


5.76 


,38.55 


5.93 


39 


40 139.61 


5.57 


39-59 
40.f>8 


5.74 


39.56 


5.91 


.39.53 


6.08 


40 
41 


41 


40.60 


5.71 


5.88 


40.55 


6.06 


40.52 


6.24 


42 


41.59 


5.85 


41.57 


6.03 


41.54 


6.21 


41.51 


6.39 


42 


43 


42.. 58 


5. 93 


42.56 


6.17 


42.53 


6.36 


42.50 


6.54 


43 


44 


43.57 


6.12 


43.54 


6.31 


43.52 


6.50 


43.49 


6.69 


44 


45 


44.56 


6.26 


44.53 


6.46 


44.51 


6.65 


44.48 


6.85 


45 


46 


45.55 


6.40 


45.52 


6.60 


45.49 


6.80 


45.46 


7.00 


46 


47 


46.54 


6.54 


46.51 


6.74 


46.48 


6.95 


146.45 


7.15 


47 


48 


47.53 


6.68 


47.50 


6.89 


47.47 


7.09 


47.44 


7.30 


48 


49 


48.52 


6.82 


48.49 


7.03 


48.46 


7.24 


48.43 


7.45 


49 


50 


49.51 


6.96 


49.48 


7.17 


49.45 


7.39 


49.42 


7.61 


50 


J 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


i 

S 

.2 

P 


82 1 


Deg. 


811 Deg. 


81,^ 


Deg. 


an Deg. 



TKAVERSE TABLE. 



19 



- 


8 Dcg. 


m Deg. 


H Deg. 


&J Dog. 





3 


Tat: 


Dep. 








1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


"51 


"50750" 


7.10 


"30:4^ 


7.~32 


50.44 


7.54 


50.41 


7.76 


51 


52 


51.49 


7.24 


51.46 


7.46 


51.43 


7.69 


51.39 


7.91 


52 


53 


52.48 


7.33 


52.4.5 


7.61 


52.42 


7.83 


52.38 


8.06 


53 


54 


53 . 47 


7.. 52 


53.44 7.75 


53.41 


7.98 


,53.37 


8.21 


54 


55 


54.46 


7.65 


.54.43 


7.89 


54.40 


8.13 


54.36 


8.37 


55 


56 


55.46 


7.79 


55.42 


8.04 


55.38 


8.28 


55.35 


8.52 


56 


57 


56.45 


7.93 


56.41 


8,18 


56.37 


8.43 


56., 34 


8.67 


57 


58 


57.44 


8.07 


57. W 


8.32 


57.36 


8.57 


57.32 


8.82 


58 


59 


.58.43 


8.21 


58.39 


8.47 


.58., 35 


8.72 


58.31 


8.98 


59 


60 


.59.42 


8.35 


59. 38 


8.61 


59.34 


8.87 


59.30 


9.13 


60 


61 


60.41 


8.49 


60.37 


8.75 


60.3.3^ 


9.02 


60.29 


9.28 


61 


62 


61.40 


8.63 


61.36 


8.90 


61.32 


9.16 


61.28 


9.43 


62 


63 


62.39 


8.77 


62.35 


9.04 


62.31 


9.31 


62.27 


9.58 


63 


64 


63.38 


8.91 


63.34 


0.18 


63.30 


9.46 


63.26 


9.74 


64 


65 


64.37 


9.05 


64.33 


9.33 


64.29 


9.61 


64.24 


9.89 


65 


66 


65.36 


9.19 


65 . 32 


9.47 


65.28 


9.76 


05.23 


10.04 


66 


67 


6f..33 


9.32 


66.31 


9.61 


66.26 


9,90 


66.22 


10.19 


67 


68 


67.. 34 


9.46 


67.30 


9.76 


67.25 


10.05 


67.21 


10.34 


68 


69 


68.33 


9.60 


68.29 


9.90 


68.24 


10.20 


68.20 


10.50 


69 


70 
71 


69.32 


9.74 


69.28 


10.04 


69.23 


10.35 


69.19 


10.65 


70 


70.31 


9.88 


70.27 


10.19 


70.22 


10.49 


70.17 


10.80 


71 


72 


71.30 


10.02 


71.25 


10.33 


71.21 


10.64 


71.16 


10.95 


72 


73 


72.29 


10.16 


72.24 


10.47 


72.20 


10.79 


72.15 


11.10 


73 


74 


73.28 


10.30 


73.23 


10.62 


73.19 


10.94 


73.14 


11.26 


74 


75 


74.27 


10.44 


74.22 


10.76 


74.18 


11.09 


74.13 


11.41 


75 


78 


75.26 


10.. 58 


75.21 


10.91 


75.17 


11.23 


75.12 


11.56 


76 


77 


76.25 


10.72 


76.20 


11.05 


76.15 


11.38 


76.10 


11.71 


77 


7S 


77.24 


10.86 


77.19 


11.19 


77.14 


11. .53 


77.09 


11.87 


78 


79 


7S.23 


10.99 


78.18 


11.34 


78.13 


11.68 


73.08 


12.02 


79 


80 
81 


79.22 


11.13 


79.17 


11.48 


79.12 


11.82 


79.07 


12.17 


80 
81 


80.21 


11.27 


80.16 


11.62 


80.11 


11.97 


80.06 


12.32 


8-Z 


81.20 


11.41 


81.15 


11.77 


81.10 


12.12 


81.05 


12.47 


82 


83 


82.19 


1 1 . 55 


82.14 


11.91 


82.09 


12.27 


82.03 


12.63 


83 


84 


83.18 


11.69 


83.13 


12.05 


83.08 


12.42 


83.02 


12.78 


84 


85 


84.17 


11.83 


84.12 


12.20 


84.07 


12.56 


84.01 


12.93 


85 


86 


85.16 


11.97 


85.11 


12.34 


85.06 


12.71 


85.00 


13.08 


86 


87 


86.15 


12.11 


86.10 


12.48 


86.04 


12.86 


8.5.99 


13.23 


87 


88 


S7.14 


12.25 


87.09 


12.63 


87.03 


13.01 


86.98 


13.39 


88 


89 


88.13 


12.39 


88.08 


12.77 


88.02 


13,. 16 


87.96 


13.54 


89 


90 
31 


89.12 


12.53 


89.07 
90.06 


12.91 


89.01 


13.30 


88.95 
89.94 


13.69 


90 
91 


90.11 


12.66 


13.08 


90.00 


13.45 


13.84 


92 


91.10 


12.80 


' 91.05 


13.20 


90.99 


13.60 


90.93 


14.00 


92 


93 


92.09 


12.94 


92.04 


13.34 


91.98 


13.75 


91.92 


14.15 


93 


94 


93.09 


13.08 


' 93.03 


13.49 


92.97 


13.89 


92.91 


14.30 


94 


95 


94.08 


13.22 


i 94.02 


13.63 


93.96 


14.04 


93.89 


14.45 


95 


96 


95.07 


13.36 


95.01 


i3.78 


94.95 


14.19 


94.88 


14.00 


96 


97 


96.06 


13.50 


96.00 


13.92 


95,93 


14.34 


95.87 


14.76 


97 


98 


97.05 


13.64 


196.99 


14.06 


96,92 


14.49 


96.86 


14.91 


98 


99 


98.04 


13.78 


! 97.98 


14.21 


97.91 


14.63 


97.85 


15.06 


99 


100 

Q 


99.03 


13.92 


98.97 


14.35 


93.90 


14.78 


98.84 


15.21 


100 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


i 

(5 


82 


[)cg. 


811 Deg-. 


8H Deg. 


8U Deg. 



20 



TRAVEKSE TABLE. 



2 

f 
1 


9Deg. 


9i Deg. 


H 


Deg. 


n Deg 


5 


Lat. 
0.99 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.16 


~0:99" 


0.16 


0.99 


0.17 


0.99 


0.17 


1 


2 


1.98 


0.31 


1.97 


0.32 


1.97 


0.33 


1.97 


0.34 


2 


3 


2.96 


0.47 


2.96 


0.48 


2.96 


0.50 


2.96 


0.51 


3 


4 


3.95 


0.63 


3.95 


0.64 


3.95 


0.66 


3.94 


0.68 


4 


5 


4.94 


0.78 


4.93 


0.80 


4.93 


0.83 


4.93 


0.85 


5 


6 


5.93 


0.94 


5.92 


0.96 


5.92 


0.99 


5.91 


1.02 


6 


7 


6.91 


1.10 


0.91 


1.13 


6.90 


1.16 


6.90 


1.19 


7 


8 


7.90 


1.25 


7.90 


1.29 


7.89 


1.32 


7.88 


1.35 


8 


9 


8.89 


1.41 


8.88 


1.45 


8.88 


1.49, 


8.87 


1.52 


9 


10 


9. 88 


1.56 


9.87 


1.61 


9.86 


1.65 


9.86 


1.69 


10 


11 


10.86 


1.72 


10.86 


1.77 


10.85 


1.82 


10.84 


1.86 


11 


12 


11.85 


1.88 


11.84 


1.93 


11.84 


1.98 


11.83 


2.03 


1 2 


13 


12.84 


2.03 


12.83 


2.09 


12.82 


2.15 


12.81 


2.20 


13 


14 


13.83 


2.19 


13.82 


2.25 


13.81 


2.31 


13.80 


2 .37 


14 


15 


14.82 


2.35 


14.80 


2.41 


14.79 


2.48 


14.78 


2.54 


15 


16 


15.80 


2.50 


15.79 


2.57 


15.78 


2.64 


15.77 


2.71 161 


17 


16,79 


2.66 


16.78 


2.73 


16.77 


2.81 


16.75 


2.88 1 17! 


18 


17.78 


2.82 


17.77 


2.89 


17.75 


2.97 


17.74 


3.05 


18 


19 


18.77 


2.97 


18.75 


3.05 


18.74 


3.14 


18.73 


3.22 


19 


20 


19.75 


3.13 


19.74 


3.21 


19.73 


3.30 


19.71 


3.39 


20 


21 


20.74 


3.29 


20.73 


3.38 


20.71 


3.47 


20.70 


3.. 56 


"21" 


22 


21.73 


3.44 


21.71 


3.. 54 


21.70 


3.63 


21.68 


3.73 


22 


23 


22.72 


3.60 


22.70 


3.70 


22.68 


3.80 


22.67 


3.90 


23 


24 


23.70 


3.75 


23.69 


3.86 


23.67 


3.96 


23.65 


4.06 


24 


25 


24.69 


3.91 


24.67 


4.02 


24.66 


4.13 


24.64 


4.23 


25 


26 


25.68 


4.07 


25.66 


4.18 


25.64 


4.29 


25.62 


4.40 


26 


27 


26.67 


4.22 


26.65 


4.34 


26.63 


4.46 


26.61 


4.57 


27 


28 


27.66 


4.38 


27.64 


4.50 


27.62 


4.62 


27.60 


4.74 


28 


29 


28.64 


4.54 


28.62 


4.66 


28.60 


4.79 


28.58 


4.91 


29 


30 
31 


29.63 


4.69 


29.61 


4.82 


29.59 


4.95 


29.57 


5.08 
5.25 


30 

31 


30.62 


4.85 


30.80 


4.98 


30.57 


5.12 


30.55 


32 


31.61 


5.01 


31.58 


5.14 


31. .56 


5.28 


31.54 


5.42 


32 


33 


32.59 


5.16 


32.57 


5.30 


32.55 


5.45 


32.52 


5.59 


33 


34 


33.58 


5.32 


33.. 56 


5.47 


33.53 


5.61 


33.51 


5.76 


34 


35 


34.57 


5.48 


34.54 


5.63 


.34.52 


5.78 


34.49 


5.93 


35 


36 


35.56 


5.63 


35.. 53 


5.79 


35.51 


5.94 


35.48 


6.10 


36 


37 


36.54 


5.79 


36.62 


5.95 


36.49 


6.11 


.36.47 


6,27 


37 


38 


37.53 


5.94 


37.51 


6.11 


37.48 


6.27 


37.45 


6.44 


38 


39 


38.52 


6.10 


38.49 


6.27 


38.47 


6.44 


38.44 


6.60 


39 


40 
41 


39.51 
40.50 


6.26 
6.41 


39.48 
40.47 


6.43 


39.45 


6.60 


39.42 


6.77 


40 
41 


6.59 


40.44 


6.77 


40.41 


6.94 


42 


41.48 


6.57 


41.45 


6.75 


41.42 


6.92 


41.39 


7.11 


42 


43 


42.47 


6.73 


42.44 


6.91 


42.41 


7.10 


42.38 


7.28 


43 


44 


43.46 


6.88 


43.43 


7.07 


43.40 


7.26 


43.36 


7,45 


44 


45 


44.45 


7.04 


44.41 


7.23 


44.38 


7.43 


44.35 


7.62 


45 


46 


45.43 


7.20 


45.40 


7.39 


45.37 


7.59 


45.34 


7.79 


46 


47 


46.42 


7.35 


46.39 


7.55 


46.36 


7.76 


46.32 


7.96 


47 


48 


47.41 


7.51 


47.38 


7.72 


47.34 


7.92 


47.31 


8.13 


48 


49 


48.40 


7.67 


48.36 


7.88 


48.33 


8.09 


48.29 


8.30 


49 


50^ 


49.38 


7.82 


49.35 


8.04 


49.32 


8.25 


49.28 


8.47 


50 

1 
ft 


1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dop. 


Lat. 


81] 


Oeg. 


801 Deg. 


801 


Deg. 


80i Dog. 



21 



i 

51 


9 Beg. 


94 Deg. 


H Deg. 


91 Deg. 


a 


Lat 


Dep. 

7.98 


Lat. 


Dep. 
~8T20 


i-"atr 


Dep. 


Lat. 


Dep. 


50.37 


"50734 


JoJiO 


8.42 


50.26 


8.64 


51 


52 


51.36 


8.13 


51.32 


8.36 


51.29 


8.58 


51.25 


8.81 


52 


53 


52.35 


8.29 


52.31 


8.52 


52.27 


8.75 


52.23 


8.98 


53 


54 


53.34 


8.45 


53,30 


8.68 


.53 . 26 


8.91 


53.22 


9.14 


54 


55 


54.32 


8.60 


54.28 


8.84 


,54.25 


9.08 


.54.21 


9.31 


55 


56 


55.31 


8.76 


55.27 


9.00 


.55.23 


9.24 


55.19 


9.48 


56 


67 


56.30' 8.92 


56.26 9.16 


56.22 


9.41 


56.18 


9.65 


57 


58 


57.29 9.07 


57.25 9.32 


57.20 


9.57 


57.16 


9.82 


58 


59 


58.27 


9.23 


58.23 9.48 


.58.19 


9.74 


.58.15 


9.99 


59 


60 


59.26 


9.39 


59.22 i 9.64 


,59.18 


9.90 


59.13 


10.16 


60 


61 


60.25^ 


9.. 54 


60.21 I 9.81 


60.16 


10.07 


60.12 


10733 


61 


62 


61.24 


9.70 


61.19 9.97 


61.15 


10.23 


61.10 


10.50 


62 


63 


62.22 


9.86 


62.18 


10.13 


62.14 


10.40 


62.09 


10.67 


63 


64 


63.21 


10.01 


63.17 


10.29 


63.12 


10.56 


63.08 


10.84 


64 


65 


64.20 


10.17 


64.15 


10.45 


64.11 


10.73 


64.06 


11.01 


65 


66 


65.19 


10.32 


65.14 


10.61 


65.09 


10.89 


65.05 


11.18 


66 


67 


66.18 


10.48 


66.13 


10.77 


66.08 


11.06 


66.03 


11.35 


67 


68 


67.16 


10.64 


67.12 


10.93 


67.07 


11.22 


67.02 


11.52 


68 


69 


68.15 


10.79 


68.10 


11.09 


68.05 


11.39 


68.00 


11.69 


69 


70 
71 


69.14 


10.95 


69.09 


11.25 


69.04 


11.55 


68.99 


11.85 
12.02 


70 

71 


70.13 


11.11 


70.08 


11.41 


70.03 


11.72 


69.97 


72 


71.11 


11.26 


71.06 


11.57 


71.01 


11.88 


70.96 


12.19 


72 


73 


72.10 


11.42 


72.05 


11.73 


72.00 


12.05 


71.95 


12.36 


73 


74 


73.09 


11.58 


73.04 


11.89 


72.99 


12.21 


72.93 


12.53 


74 


75 


74.08 


11.73 


74.02 


12.06 


73.97 


12.. 38 


73.92 


12.70 


75 


76 


75.06 


11.89 


75.01 


12.22 


74.96 


12.. 54 


74.90 


12.87 


76 


77 


76.05 


12.05 


76.00 


12.38 


75.94 


12.71 


75.89 


13.04 


77 


78 


77.04 


12.20 


76.99 


12.. 54 


76.93 


12.87 


76.87 


13.21 


78 


79 


78.03 


12.36 


77.97 


12.70 


77.92 


13.04 


77.86 


13.38 


79 


80 


79.02 


12.51 


78.96 


12.86 


78.90 


13.20 


78.84 


13.55 


80 

81 


81 


80.00 


12.67 


79.95 


13.02 


79.89 


13.37 


79.83 


13.72 


82 


80.99 


12.83 


80.93 


13.18 


80.88 


13.53 


80.82 


13.89 


82 


83 


81.98 


12.98 


81.92 


13.34 


81.86 


13.70 


81.80 


14.06 


83 


84 


82.97 


13.14 


82.91 


13.50 


82.85 


13.86 


82.79 


14.23 


84 


85 


83.95 


13.30 


83.89 


13.66 


83.83 


14.03 


83.77 


14.39 


85 


86 


84.94 


13.45 


84.88 


13.82 


84.82 


14.19 


84.76 


14.. 56 


86 


87 


85.93 


13.61 


85.87 


13.98 


85.81 


14.36 


85.74 


14.73 


87 


88 


86.92 


13.77 


86.86 


14.15 


86.79 


14.. 52 


86.73 


14.90 


88 


89 


87.90 


13.92 


87.84 


14.31 


87.78 


14.69 


87.71 


15.07 


89 


90 


88.89 


14.08 


88.83 


14.47 


88.77 


14.85 


88.70 


15.24 


90 
91 


91 


89.88 


14.24 


89.82 


14.63 


89.75 


15.02 


89.69 


15.41 


92 


90.87 


14.39 


90.80 


14.79 


90.74 


15.18 


90.67 


15.58 


92 


93 


91.86 


14.55 


91.79 


14.95 


91.72 


15.35 


91.66 


15.75 


93 


94 


92.84 


14.70 


92.78 


15.11 


92.71 


15.51 


92.64 


15.92 


94 


95 


93.83 


14.86 


93.76 


15.27 


93.70 


15.68 


93.63 


16.09 


95 


96 


94.82 


15.02 


94.75 


15.43 


94.68 


15.84 


94.61 


16.26 


96 


97 


95.81 


15.17 


95.74 


15.59 


95.67 


16.01 


95.60 


16 43 


97 


98 


96.79 


15.33 


96.73 


15.75 


96.66 


16.17 


96.58 


16.60 


98 


99 


97.78 


15.49 


97.71 


15.91 


97.64 


16.34 


97.57 


16.77 


99 


100 

s 

a 
1 


98.77 


15.64 


98.70 


16.07 


98.63 


16.50 


98.56 


16.93 


100 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Q 


81 Deg. 


801 Deg. 


80^ Deg. 


80i Deg. 



22 



TRAVERSE TABLE. 



p 


10 1 
Lat. 


"DepT 


lOi Deg. 


10^ 


Deg. 


10| Deg. 


i 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


"oTos' 


0.17 


"0798 


1)718 


"OAiS 


q7i8 


"6798" 


0.19 


1 


2 


1.97 


0..35 


1.97 


0.36 


1.97 


0.36 


1.96 


0.37 


2 


3 


2.95 


0.52 


2.95 


0.53 


2.95 


0.55 


2.95 


56 


3 


4 1 3 . 94 


0.69 


3.94 


0.71 


3.93 


0.73 


3.93 


0.75 


4 


5 4 . 92 


0.87 


4.92 


0.89 


4.92 


0.91 


4.91 


0.93 


5 


6 i 5.91 


1.04 


5.90 


1.07 


5.90 


1.09 


5.89 


J. 12 


6 


7 


6.89 


1.22 


6.89 


1.25 


6.88 


1.28 


6.88 


1.31 




8 


7.88 


1.39 


7.87 


1.42 


7.87 


1.46 1 


7.86 


1.49 


8 


9 


8.86 


1.56 


8.86 


1.60 


8 . 85 


1.64 


8.84 


1.68 


9 


10 


9.85 


1.74 


9.84 


1.78 


9.83 
10.82 


1.82 


9.82 


1.87 


10 
11 


11 [10.83 


1.91 


10.82 


1 .96 


2.00 


10.81 2.05 


12 11.82 


2.08 


11.81 


2.14 


11.80 


2.19 


11.79 


2.24 


12 


13 i 12.80 


2.26 


12.79 


2.31 


12.78 


2.37 


12.77 


2.42 


13 


14 


13.79 


2.43 


13.78 


2.49 


13.77 


2.55 


13.75 


2.61 


14 


1.5 


14.77 


2.60 


14.76 


2.67 


14.75 


2.73 


14.74 


2.80 


15 


16 


15.76 


2.78 


15.74 


2.85 


15.73 


2.92 


15.72 


2.98 


16 


17 


16.74 


2.95 


16.73 


3.03 


16.72 


3.10 


16.70 


3.) 7 


17 


18 


17.73 


3.13 


lV.71 


3.20 


17.70 


3.28 


17.6'8 


3.36 


18 


19 


18.71 


3.30 


18.70 


3.38 


18.68 


3.46 


18.67 


3.54 


19 


20 

21 


19.70 
20.68 


3.47 
3.65 


19.68 


3.56 
3.74 


19.67 


3.64 


19.65 
20763' 


3.73 

3.92" 


20 
21 


20.66 


20.65 


3.83' 


22 21.67 


3.82 


21.65 


3.91 


21.63 


4.01 


21.61 


4.10 


22 


23 


22.65 


3.99 


22 . 63 


4.09 


22.61 


4.19 


22 . 60 


4.29 


23 


24 


23.64 


4.17 


23.62 


4.27 


23.60 


4.37 


23 . .58 


4.48 


24 


2.5 


24.62 


4.34 


24.60 


4.45 


24.58 


4.56 


24.56 


4.66 


25 


26 


25.61 


4.51 


25.59 


4.63 


25.56 


4.74 


25.. 54 


4.85 


26 


27 


26.59 


4.69 


26.57 


4.80 


26.. 55 


4.92 


26.153 


5.04 


27 


28 


27.57 


4.86 


27.55 


4.98 


27.. 53 


5.10 


27.51 


5.22 


28 


29 


28.56 


5.04 


28.. 54 


5.16 


28.51 


5.28 


28.49 


5.41 


29 


30 


29.54 


5.21 


29.52 


5.34 


29.. 50 


5.47 


29.47 


5 . 60 


30 


31 


30.. 53 


5.38 


30.51 


5.52 


30.48 


5.65" 


.30.46 


" 5.78 


3l 


32 


31.51 


5.56 


31.49 


5.69 


31.46 


5.83 


31.44 


5.97 


32 


33 


32.. 50 


5.73 


32.47 


5.87 


32.45 


6.01 


32.42 


6.16 


33 


34 


33.48 


5.90 


33.46 


6.05 


33.43 


6.20 


33.40 


6.34 


34 


3.5 


34.47 


6.08 


34.44 


6.23 


34.41 


6.38 


34.39 


6.. 53 


35 


36 


35.45 


6.25 


35.43 


6.41 


35.40 


6.56 


35.37 


6.71 


36 


37 


36.44 


6.42 


36.41 


6.58 


36.38 


6.74 


36.. 35 


6.90 


37 


38 


37.42 


6.60 


37.39 


6.76 


37.36 


6.92 


37.33 


7.09 


38 


39 


38.41 


6.77 


.38.38 


6.94 


38.35 


7.11 


38.32 


7.27 


39 


40 
41 


39.39 


6.95 


39.36 


7.12 


39.33 


7.29 


39.30 


7.46 


40 
41 


40.38 


7.12 


40.35 


7.30 


40.31 


"7747 


40.28 


7.65 


42 


41.36 


7.29 


41.33 


7.47 


41.30 


7.65 


41.26 


7.83 


42 


43 


42.35 


7.47 


42.31 


7.65 


42.28 


7.84 


42.25 


8.02 


43 


44 


43.33 


7.64 


43.30 


7.83 


43.26 


8.02 


43.23 


8.21 


44 


45 


44.32 


7.81 


44.28 


8.01 


44.25 


8.20 


44.21 


8.39 


45 


46 


45.30 


7.99 


45.27 


8.19 


45.23 


8.38 


45.19 


8.. 58 


46 


47 


46.29 


8.16 


46.25 


8.36 


46.21 


8.57 


46.18 


8.77 


47 


48 


47.27 


8.34 


47.23 


8.. 54 


47.20 


8.75 


47.16 


8.95 


48 


49 


48.26 


8.51 


48.22 


8.72 


48.18 


8.93 


48.14 


9.14 


49 


50 


49.24 


8.68 


49.20 


8.90 


49.16 


9.11 


49.12 


9.33 


50 

i 

s 


~8 

.2 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


80 1 


Deg. 


791 


Deg. 


791 Deg. 


79i 


Deg. 



TtiAVEKSE lARLE. 



23 



3 


10 Deg. 


m Deg. 


lOi Deg. 


101 Deg. 


O 

1 

9 
~5T 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dcp. 


Lat. 


Dep. 


TT 


50.23 


8.86 


50.19 


9.08 


50.15 


9.29 


.50.10 


9.51 


52 


51.21 


9.03 


51.17 


9.25 


51.13 


0.48 


51.09 


9.70 


52 


53 


52.19 


9.20 


52.15 


9.43 


.52.11 


9.66 


52.07 


9.89 


53 


54 


53.18 


9.38 


53.14 


9.61 


53.10 


9.84 


.53.05 


10.07 


54 


65 


54.16 


9.55 


54.12 


9.79 


54.08 


10.02 


.54.03 


10.26 


55 


56 


55.15 


9.72 


55.11 


9.96 


55.06 


10.21 


55.02 


10.45 


56 


57 


56.13 


9.90 


56.09 


10.14 


56.05 


10.39 


56.00 


10.63 


57 


58 


.57.12 


10.07 


,57.07 


10.32 


.57.03 


10.57 


,56.98 


10.82 


58 


59 


58.10 


10.25 


.58.06 


10.50 


■58.01 


10.75 


57.96 


11.00 


59 


60 


59.09 1 10.42 


59.04 1 10.68 


59.00 


10.93 


.58.95 
59.93 


11.19 


60 
~61 


61 60.07 110.59 


60.03' 10.85 


.59.98 


11.12 


11.38' 


62 61.06 i 10.77 


61.01 11.03 


60.96 


11.30 


60.91 


11. .56 


62 


63 62.04 


10.94 


61.99 ' 11.21 


61.95 


11.48 


61.89 


11.75 


63 


64 


63.03 


11.11 


62.98 1 11.39 


62.93 


11.66 


62.88 


11.94 


64 


65 


64.01 


11.29 


63.96 11.57 


63.91 


11.85 


63.86 


12.12 


65 


66 


65.00 


11.46 


64.95 11.74 


64.89 


12.03 


64.84 


12.31 


66 


67 


65.98 


11.63 


65.93 


11.92 


65.88 


12.21 


65.82 


12.50 


67 


68 


66.97 


11.81 


66.91 


12.10 


66.86 


12.39 


66.81 


12.68 


68 


69 


67.95 


11.98 


67.90 


12.28 


67.84 


12.57 


67.79 


12.87 


69 


70 
71 


68.94 


12.16 


68.88 12.46 


68.83 


12.76 


68.77 


13.06 


70 
75 


69.92 


12.33 


69.87 1 12.63 


69.81 


12.94 


69.75 


13.24 


72 


70.91 12.50 


70.85 i 12.81 


70.79 


13.12 


70.74 


13.43 


72 


73 


71.89 12.68 


71.83 '' 12.99 


71.78 


13.30 


71.72 


13.62 


73 


74 


72.88 12.85 


72.82 i 13.17 


72.76 


13.49 


72.70 


13.80 


74 


75 


73.86 13.02 


73.80 


13.35 


73.74 


13.67 


73.68 


13.99 


75 


76 


74.85 1 13.20 


74.79 


13.52 


74.73 


13.85 


74.67 


14.18 


76 


77 


75.83 


13.37 


75.77 


13.70 


75.71 


14.03 ; 75.65 


14.36 


77 


78 


76.82 


13.54 


76.76 


13.88 


76.69 


14.21 


76.63 


14.55 


78 


79 


77.80 


13.72 


77.74 


14.06 


77.68 


14.40 


77.61 


14.74 


79 


80 
81 


78.78 


13.89 


78.72 


14.24 


78.66 


14.. 58 


78.60 


14.92 


80 
81 


79.77 


14.07 


79.71 


14.41 


79.64 


14.76 


79.58 


15. if 


82 


80.75 


14.24 


80.69 


14.. 59 


80.63 


14.94 


80.50 


15.29 


82 


83 


81.74 


14.41 


81.68 


14.77 


81.01 


15.13 


81.54 


15.48 


83 


84 


82.72 


14.59 


82.66 


14.95 


82.59 


15.31 


82.53 


15.67 


84 


85 


83.71 


14.76 


83.64 


15.13 


83.. 58 


15.49 


83.51 


15.85 


85 


86 


84.69 


14.93 


84.63 


15.30 


84.56 


15.67 


84.49 


16.04 


86 


87 


85.68 


15.11 


85.61 


15.48 


85.54 


15.85 


85.47 


16.23 


87 


88 


86.66 


15.28 


86.60 


15.66 


86.53 


16.04 


8'3.46 


16.41 


88 


89 


87.65 


15.45 


87.58 


15.84 


87.51 


16.22 


87.44 


16.60 


89 


90 
91 


88.63 
89.62' 


15.63 


88.56 


16.01 


88.49 


16.40 


88.42 


16.79 
16.97 


90 
91 


15.80 


89., 55 


16.19 


89.48 


16. 5S 


89.40 


92 


90.60 


15.98 


90.53 


16.37 


90.46 


16.77 


90.39 


17.16 


92 


93 


91.59 


16.15 


91.52 16.55 


91.44 


16.95 


91.37 


17.35 


93 


94 


92.57 


16.32 


92.. 50 


16.73 


92.43 


17.13 


92.35 


17.53 


94 


95 


93.56 


16.50 


93.48 


16.90 


93.41 


17.31 


93.33 


17.72 


95 


96 


94.54 


16.67 


94.47 


17.08 


94.39 


17.49 


94.32 


17.91 


96 


97 


95.53 


16.84 


95.45 


17.26 


95.38 


17.68 


95.30 


18.09 


97 


98 


96.51 


17.02 


96.44 


17.44 


96.36 


17.86 


96.23 


18.28 


98 


99 


97.50 


17.19 


97.42 


17.62 


97.34 


18.04 


97.26 


18.47 


99 


100 

T 
s 


98.48 


17.36 


98.40 


17.79 


98.33 


18.22 


98.25 


18.65 


100 

.2 
Q 

1 


Dcp. 


Lat. 


Dep. 1 Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


80 Deg. 


79i Deg. 


79j Deg. 


79i Deg. 



24 



TRAVERSE TABLE. 



I 


11 Deg. 


lU Deg. 


Hi 


Deg. 


Ill Deg. 


? 
? 

1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


~Y 


0.98 


0.19 


0,98 


0.20 


0.98 


0.20 


0.98 


nr.20- 


2 


1.96 


0,38 


1,96 


0.39 


1.96 


0.40 


1.96 


0.41 


2 


3 


2.94 


0.57 


2,94 


0.59 


2,94 


0.60 


2.94 


0.61 


3 


4 


3.93 


0.76 


3,92 


0.78 


3,92 


0.80 


3.92 


0.82 


4 


5 4.91 


0,95 


4,90 


0.98 


4,90 


1.00 


4.90 


1.02 


5 


6 


5.89 


1,14 


5,88 


1.17 


5.88 


1.20 


5.87 


1.22 


6 


7 


6.87 


1,34 


6,87 


1.37 


6.86 


1.40 


6.85 


1.43 


7 


8 


7.85 


1.53 


7,85 


1.56 


7.84 


1.59 


7.83 


1.63 


8 


9 


8.83 


1,72 


8,83 


1.76 


8,82 


1,79 


8.81 


1.83 


9 


10 


9.82 


1.91 


9,81 


1.95 


9,80 


1.99 


9.79 


2.04 


10 
11 


11 


10.80 


2.10 


10,79 


2.15 


10.78 


2.191 


10.77 


2.24 


12 


11.78 


2.29 


11,77 


2.34 


11,7-6 


2.39 


11.75 


2.44 


12 


13 


12.76 


2.48 


12,75 


2.54 


12,74 


2.59 


12.73 


2.65 


13 


14 


13.74 


2.67 


13.73 


2.73 


13.72 


2.79 


13.71 


2.85 


14 


15 


14.72 


2.86 


14.71 


2.93 


14.70 


2.99 


14.69 


3.06 


15 


16 


15.71 


3,05 


15.69 


3.12 


15.68 


3.19 


15.66 


3.26 


16 


17 


16.69 


3,24 


16.67 


3.32 


16.66 


3.39 


16.64 


3.46 


17 


18 


17.67 


3,43 


17.65 


3.51 


17.64 


3.. 59 


17.62 


3.66 


18 


19 


18.65 


3,63 


18,63 


3.71 


18.62 


3.79 


18.60 


3.87 


19 


20 


19.63 
20.61 


3,82 
4,01 


19.62 


3.90 

-4TT0- 


19.60 


3.99 


19.58 


4.07 


20 


21 


30,60 


20.. 58 


4.19 


20 . 50 


4.28 


' 21 


22 


21.60 


4,20 


21,58 


4.29 


21.56 


4.39 


21.54 


4.48 


23 


23 


22.58 


4,39 


22,56 


4.49 


22.54 


4.. 59 


22.52 


4.68 


23 


24 


23.56 


4,58 


23,54 


4.68 


23.52 


4.78 


23.50 


4.89 


24 


25 


24.54 


4.77 


24,52 


4.88 


24.50 


4.98 


24.48 


5.09 


25 


26 


25.52 


4.96 


25,50 


5.07 


25.48 


5.18 


25.46 


5.30 


26 


27 


20.50 


5.15 


26,48 


5.27 


26.46 


5.38 


26.43 


5.. 50 


27 


28 


27.49 


5.34 


27.46 


5.46 


27.44 


5,58 


27.41 


5.70 


28 


29 


28.47 


5.53 


28,44 


5.66 


28.42 


5,78 


28.39 


5.91 


29 


30 


29.45 


5.72 


29,42 
30,40 


5.85 
6.05 


29,40 


5.98 


29.37 


6.11 


30 


31 


30.43 


5.92 


30,38 


6.18 


30.35 


6.31 


31 


32 


31.41 


6.11 


31,39 


6.24 


31,36 


6.38 


31.33 


6.52 


32 


33 


32.39 


6-30 


32,37 


6.44 


32.34 


6.58 


32.31 


6.72 


33 


34 


33.38 


6.49 


33.35 


6.63 


33.32 


6.78 


33.29 


6.92 


34 


35 


34.36 


6.68 


34.33 


6.83 


34.30 


6.98 


34.27 


7.13 


35 


36 


35.34 


6.87 


35.31 


7.02 


.35.28 


7.18 


35.25 


7.33 


36 


37 


36.32 


7.06 


36.29 


7.22 


36.26 


7.38 


36.23 


7.53 


37 


38 


37.30 


7.25 


37.27 


7.41 


37.24 


7.58 


37.20 


7.74 


38 


39 


33.28 


7,44 


38.25 


7.61 


38.22 


7.78 


38.18 


7.94 


39 


40 


39.27 


7,63 


39,23 


7,80 


39.20 


7.97 


39.16 


8.15 


40 
41 


41 


40.25 


7.82 


40,21 


8,00 


40.18 


8.17 


40.14 


8 .35 


42 


41.23 


8.01 


41,19 


8,19 


41.16 


8.37 


41.12 


8.55 


42 


43 


42.21 


8.20 


42.17 


8.39 


42.14 


8.57 


42.10 


8.76 


43 


44 


43.19 


8.40 


43.15 


8.58 


43.12 


8.77 


43.08 


8.96 


44 


45 


44.17 


8.59 


44.14 


8.78 


44.10 


8.97 


44.06 


■9.16 


45 


46 


45.15 


8.78 


45.12 


8.97 


45.08 


9.17 


45.04 


9.37 


46 


47 


46.14 


8.97 


46.10 


9.17 


46.06 


9.37 


46.02 


9.57 


47 


48 


47.12 


9.16 


47.08 


9.36 


47.04 


9.57 


46.99 


9.78 


48 


49 


48.10 


9.35 


48.06 


9.. 50 


48.02 


9.77 


47.97 


9.98 


49 


1 


49.08 


9,54 


49.04 


Lat. 
Da^. 


49.00 


9.97 


48.95 


10.18 


50 


Dep. 


Lat, 


Dep. 

781 


Dep. 


Lat. 


Dep. 


Lat. 


i 


79] 


Deg, 


'8^ 


Deg. 


78i Deg, 



TKAVEKSE TABLE. 



25 



a 
§ 

51 


11 Deg, 


Hi Def, 


11^ Deg. 


Ill Deg. 


~51 


Lat. 


1 Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 Lat. 1 Dep, 


50,06 


9.73 


50,02 


9.95 


49.98 


10.17 


49.93 10.39 


52 


51.04 


9.92 


51,00 


10.14 


50.96 


10.. 37 


1 50,91 


10.59 


52 


53 


52.03 


10.11 


51,98 


10.34 


51,94 


10.57 


51,89 


10.79 


53 


51 


53.01 


10.30 


52.96 


10.. 53 


62.92 


10.77 


52.87 


11.00 


54 


55 


53.99 


10.49 


53.94 


10.73 


53.90 


10.97 


53.85 


11.20 


55 


56 


54.97 


10.69 


54.92 


10.93 


64.88 


11.16 


54.83 


11.40 


56 


57 


55.95 


10.88 


55.90 


11.12 


55.86 


11.36 


55.81 


11.61 


57 


58 


56 . 93 


11.07 


56.89 


11.32 


56.84 


11.56 


56.78 


11.81 


58 


59 


57.92 


11.26 


57.87 


11.51 


57.82 


11.76 


57.76 


12.01 


59 


60 

6'l 


58.90 


11.45 


.58 . 85 
59.83 


11.71 


58.80 


11.96 


58.74 


12.22 


60 

~6l 


59.88 


11.64 


11.90 


59.78 


12.16 


59 . 72 


12.42 


63 


60.86 


11.83 


60.81 


12.10 


60.76 


12.36 


60.70 


12.63 


62 


63 


61.84 


12.02 


61,79 


12.29 


61.74 


12.56 


61,68 


12.83 


63 


64 


62.82 


12.21 


62.77 


12.49 


62.72 


12.76 


62,66 


13.03 


64 


65 


63.81 


12.40 


63,75 


12.68 


63.70 


12.96 


63,64 


13.24 


65 


66 


64.79 


12.59 


64,73 


12.88 


64.68 


13.16 


64.62 


13.44 


66 


67 


65.77 


12.78 


65,71 


13.07 


65.66 


13.36 


65,60 


13.64 


67 


68 


66.75 


12.98 


66,69 


13.27 


66.63 


13.56 


66.58 


13.85 


68 


69 


67.73 


13.17 


67,67 


13.46 


67.61 


13.76 


67,55 


14.05 


69 


70 
71 


68.71 


13.36 


68,66 


13.66 


68.59 


13.96 


68,53 


14.25 


70 


69.70 


13.55 


69,64 


13.85 


69.57 


14.16 


69,51 


14.46 


71 


72 


70.68 


13.74 


70,62 


14,05 


70.55 


14.35 


70.49 


14.66 


72 


73 


71.66 


13.93 


71.60 


14,24 


71.53 


J 4. 55 


71.47 


14.87 


73 


74 


72.64 


14.12 


72.58 


14.44 


72.51 


14.75 


72.45 


15.07 


74 


75 


73.62 


14.31 


73.56 


14.63 


73.49 


14.95 


73.43 


15.27 


75 


76 


74.60 


14.50 


74.54 


14.83 


74.47 


15.15 


74.41 


15.43 


76 


77 


75.59 ! 14.69 


75.52 


15.02 


75.45 


15.35 


75 39 


15.68 


77 


78 


76.57 


14.88 


76.50 


15.22 


76.43 


15.55 


76.37 


15.88 


78 


79 


77.55 


15.07 


77.48 


15.41 


77.41 


15.75 


77.34 


16.09 


79 


80 
81 


78.53 


15.26 
15,46 


78.46 1 15.61 


78.39 


15.95 


78.32 


16.29 


80 


79.51 


79.44 


15.80 


79.37 


16.15 


79.30 


16.49 


TT 


82 


80.49 


15,65 


80,42 


16.00 


80.35 


16.35 


80.28 


16.70 


82 


83 


81.48 


15,84 


81,41 


16.19 


81.33 


16.55 


81.26 


IB. 90 


83 


84 


82.46 


16.03 


82,39 


16.39 


82.31 


16.75 


82.24 


17.11 


84 


85 


83.44 


16,22 


83,37 


16.58 


83.29 


16.95 


83.22 


17.31 


85 


86 


84.42 


16,41 


84.35 


16.78 


84.27 


17.15 


84.20 17.51 


86 


87 


85.40 


16.60 


85.33 


16.97 


85.25 


17.35 


85.18 


17.72 


87 


83 


86.38 


16.79 


86.31 


17,17 


86.23 


17.54 


86.16 


17.92 


88 


89 


87.36 


16.98 


87.29 


17,36 


87.21 


17.74 


87.14 


18.12 


89 


90 
91 


88.35 


17.17 


88.27 


17,56 


88.19 


17.94 


88.11 


18.33 


90 


89.33 


17.36 


89.25 


17,75 


89.17 


18.14 


89.09 


18.53 


91 


92 


90.31 


17.55 


90.23 


17,95 


90.15 


18.34 


90.07 


18.74 


92 


93 


91.29 


17.75 


91.21 


18.14 


91.13 


18.54 


91.05 


18.94 


93 


94 


92.27 


17.94 


92.19 


18,34 


92.11 


18.74 


92.03 


19.14 


94 


95 


93.25 


18.13 


93.17 


18.53 


93.09 


18.94 


93.01 


19.35 


95 


96 


94.24 


18.32 


94.16 


18.73 


94.07 


19.14 


93.99 


19.55 


96 


97 


95.22 


18.51 


95.14 


18.92 


95.05 


19.34 


94.97 


19.75 


97 


98 


96.20 


18.70 


96.12 


19.12 


96.03 


19.54 


95.95 


19.96 


98 


99 


97.18 


18.89 


97.10 


19.31 


97.01 


19.74 


96.93 


20.16 


99 


100 


98.16 


19.08 


98.08 


19.51 


97.99 


19.94 


97.90 


20.36 lOOf 


Dep. 


Lat. 


Dep. 


Lat. 


Dep, 


Lat. 


Dep. 


Lat. 


1 


79 Deg. 


781 Deg. 


78|Deg. 


m Deg. 



26 



TRAVERSE TABLE. 



1 


12Deg 


12i Deg. 


m. 


Deg. 


124 Deg. 




K 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


3 


r 


0.98 


0.21 


~0798" 


0,21 


0.98 


0,22 


0,98 


0,22 


1 


2 


1.96 


0.42 


1.95 


0.42 


1.95 


0.43 


1.95 


0.44 


2 


3 


2.93 


0.62 


2.93 


0.64 


2.93 


0.65 


2,93 


0.66 


3 


4 


3.91 


0.83 


3.91 


0.85 


3.91 


0,87 


3.90 


0.88 


4 


5 


4.89 


1.04 


4.89 


1.06 


4.88 


1,08 


4.88 


I.IO 


5 


6 


5.87 


1.25 


5.86 


1.27 


5.86 


1.30 


5,85 


1.32 


6 


7 


6.85 


1.46 


6.84 


1.49 


6.83 


1,52 


6.83 


1.54 


7 


8 7.83 


1.66 


7.82 


1.70 


7.81 


1,73 


7,80 


1.77 


8 


9 8.80 


1.87 


8.80 


1.91 


8.79 


1.95 


8,78 


1.99 


9 


10 9.78 


2.08 


9.77 


2.12 


9.76 


2,16 


9,75 


2.21 


10 


11 in.7G 


2.29 


10.75 


2.33 


10.74 


2.38 


10.73 


2,43 


11 


12 11.74 


2.49 


11.73 


2.55 


1 1 . 72 


2.60 


1 1 , 70 


2.65 


12 


13 12.72 


2.70 


12.70 


2.76 


12.69 


2.81 


12,68 


2,87 


13 


14 13.09 


2.91 


13.68 


2.97 


13.67 


3,03 


13.65 


3,09] 14 


15 . 14.67 


3.12 


14.66 


3.18 


14.64 


3.25 


14,63 


3,31 15 


16 15.05 


3.. 33 


15.64 


3.39 


15.62 


3,40 


15.61 


3.. 53 1 16 


17 16.63 


3.. 53 


16.61 


3.61 


16.60 


3.68 


16.58 


3.75! 17 


18 17.61 


3.74 


17.59 


3.82 


17. .57 


3,90 


17.. 06 


3.97 ! 18 


19 18.53 


3.95 


18.57 


4.03 


18.55 


4.11 


18.. 53 


4.19 19 


20 


19.56 


4.16 


19.54 
20.52 


4.24 


19.53 


4.33 


19,51 
20,48 


4.41 ! 20 


21 


20 . 54 


4.37 


4.46 


20 . 50 


4.5.5 


4,63 


21 


22 2 1 . 52 


4.57 


21.50 


4.67 


21.48 


4.76 


21.46 


4,86 




23! 22.. 50 


4.78 


22.48 


4.88 


22.45 


4.98 


22.43 


5,08 


23 


24 123.48 


4.99 


23.45 


5.09 


23.43 


5.19 


23.41 


5.30 


24 


25 


24.45 


5.20 


24.43 


5.30 


24.41 


5.41 


24,38 


5.. 52 


25 


26 


25.43 


5.41 


25.41 


5.52 


25. 3S 


5.63 


25,36 


5,74 


26 


27 


26.41 


5.61 


26.39 


5.73 


26.30 


5.84 


26.33 


5,96 


27 


28 


27.. 39 


5.82 


27.36 


5.94 


27.34 


6.06 


27.31 


6,18 


28 


29 


28 . 37 


6.03 


28 . 34 


6.15 


28.31 


6.28 


28.28 


6.40 


29 


30 


29.34 


6.24 


29.32 
.30.29^ 


6.37 
6.. 58 


29.29 


6.49 


29,26 


6 . 62 


30 


31 30.32 


6.45 


,30.27 


6.71 


30,24 


6,84 


31 


32 31.30 


6.65 


31.27 


6.79 


31.24 


6.93 


31,21 


7,06 


32 


33 32.28 


6.86 


32 . 25 


7.00 


32 . 22 


7.14 


32.19 


7,28 


33 


34 33.26 


7.07 


33.23 


7.21 


33.19 


7.36 


33,16 


7.50 


34 


35 34.24 


7.28 


.34.20 


7.43 


,34.17 


7,. 58 


134.14 


7.72 


35 


36 35.21 


7.48 


35.18 


7.64 


35.15 


7.79 


135,11 


7,95 


36 


37 , 36.19 


7.69 


36.16 


7.85 


36.12 


8,01 


136,09 


8,17 


37 


38 137.17 


7.90 


37.13 


8.06 


37.10 


8,22 


i 37,06 


8,39 


38 


39 


38.15 


8.11 


38 . 1 1 


8.27 


38.08 


8 44 


138,04 


8,61 


39 


40 


39.13 


8.32 


39.09 
40:07^ 


8.49 


39.05 


8,66 

8,87 


i 39.01 


8.83 
9.05 


40 
41 


41 


40.10 


8.52 


8.70 


40.03 


39.99 


42 


4[.08 


8.73 


41.04 


8.91 


41.00 


9.09 


40,96 


9.27 


42 


43 142.06 


8.94 


42.02 


9.12 


41,98 


9.31 


41.94 


9.49 


43 


44 143.04 


9.15 


43.00 


9.34 


42.96 


9.. 52 


42.92 


9.71 


44 


45 144.02 


9.36 


43.98 


9.55 


43.93 


9.74 


43,89 


9.93 45 


46 44.99 


9.56 


44.95 


9.76 


44.91 


9,96 


U4.87 


10.15 46 


47 45.97 


9.77 


45.93 


9.97 


45.89 


10,17 


45.84 


10.37 47 


48 46.95 


9.98 


46.91 


10.18 


46.86 


10,39 


'46.82 


10,. 59 48 


49 47.93 


10.19 


47.88 


10. lO 


47.84 


10,61 


47.79 


10.81 1 49 


50 


48.91 


10.40 


48.86 


10.61 


48.81 


10.82 


48.77 


11,03 1 50 


1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat, 


1 

Q 


78 


Deg. 


771 


Deg. 


771 


Deg, 


77i Deg. 



TRAVERSE TABLE. 



27 



"5i 


12 Deg. 


12i Deg. 


12i Deg. 


12| Deg. 




Lat. 1 Dup. 
49.89 'To. (30 


Lat. ; Dep. 


Lat. Dep. 


Lat. 


Dep. 


49.84 1 10.82 


49.79 ! 11.04 


49.74 


11.26 


52 


50.86, 10.8] 


50.82 11.03 


50.77 


11.25 


50.72 


11.48 i 52} 


53 


51.84 1 11.02;! 51.79 1 11.25 


151.74 


11.47 51.69 


11.70 .53 


54 


.52.82' 11.23 


.52.77 : 11.46 


152.72 


11.69 52.67 ! ll.L'2 '. 54 | 


55 


53.80 , 11.44 


.53.75 11.67 


1 53.70 


11.90 .53.64 '•■ 12.14 I 55 1 


56 


.54.78 ; 11.64 


54.72 1-11.88 


54.67 


12.12 .54.62 


12.36 1 5ti 


57 


55.75 1 11.85 


.55.70 12.09 


155.65 '12.34 II 55.. 59 


12..'}8 i 67 


5S 


56.73 1 1,2.06 


56.68 12.31 


56.63 ; 12.55 II 56.67 


12.80 58 


59 


57.71 12.27 


57.66 12.52 


57.60 


l".i.77 II 57.55 


13.02 1 59 




58.69 1 12.47 


53.63 12.73 
.59.61 12.94 


1 58.58 
■59.55 


12.99 


58.52 


13.24! 60 


59.67 


12.68 


13.20 


59.50 


13.46 1 61 


6-2 


60 , 65 


12.89 


60.59 i 13. 16 


160.53 


13.42 


60.47 


13.68 i 62 


G:j 


61.62 


13.10 


61.57 ; 13.37 


61.51 


13.64 


61.45 


13.90 1 63 


64 


62.60 


13.31 


62.54 i 13.58 


.62.48 


13.85 


62.42 


14.12 


64 


65 


63.58 


13.51 


63.52 13.79 


63 .46 


14.07 


63.40 


14.35 


65 


66 


fi4.56 


13.72 


64.50 14.00 


164.44 


14.29 


64.37 


14.57 


06 


67 


6 5.. 54 


13.93 


65.47 I 14.22 


; 65.41 


14.50 


65.35 


14.79 


67 


6S 


65.51 


14.14 


66.45 


14.43 


166.39 


14.72 


60.32 


15.01 


68 


69 


67.49 


14.35 


67.43 


14.64 


67.36 


14.93 


67.30 


15.23 


69 


70 


tiS.47 


14.55 


68.41 
69.38 


14.85 
15.06 


[68.34 
69.32 


15.15 


68.27 


15.45 
15.67 


70 

71 


69.45 


14.76 


15.37 


69.25 


T2 


70.43 ' 14.97 


70.36 


15.28 


70.29 


15.58 


70.22 


16.89 


72 


73 


71.40 ' 15.18 


71.34 


15.49 


71.27 


15.80 


71.20 


16.11 


73 


74 


72. 3S: 15.39 


72.32 


15.70 


72.25 


16.02 


72.18 


16.33 


74 


75 


73.36 1 15.59 


73.29 


15.91 


73.22 


16.23 


73.15 


16.55 


75 


76 


74.34 j 15,80 


74.27 


16.13 


74.20 


16.45 


74.13 


16.77 


76 


77 


75.32 1 16.01 


75.25 


16.34 


75.17 


16.67 


75.10 


16.99 


77 


78 


76.30 1 16.22 


76.22 


16.55 


76.15 


16.88 


76.08 


17.21 


78 


79 


77.27 ! 16.43 


77.20 


16.76 


77.13 


17.10 


77.05 


17.44 


79 


80 
81 


78.25! 16.63 


78.18 
79.16 


16.97 


78.10 
79.08 


17.32 


78.03 


17.66 


80 
81 


79.23 


16.84 


17.19 


17.. 53 


79.00 


17.88 


82 


80.21 


17.05 


80.13 


17.40 


80.06 


17.75 


75.98 


18.10 


82 


83 


81.19 


17.26 


81.11 


17.61 


81.03 


17.96 


80.95 


18.32 


83 


84 


82.16 


17.46 


82.09 


17.82 


82.01 


18.18 


81,93 


18.54 


84 


85 


83.14 


17.67 


83.06 j 18.04 j 


82.99 


18.40 


82.90 


18.76 


85 


86 


84.12 


17.88 


84.04 i 18.25 1 


83.96 


18.61 


83.88 


18.98 


86 


87 


85.10 


18.09 


85.02 


18.46 


84.94 


18.83 


84.85 


19.20 


87 


88 


86.08 


18.30 


86.00 


18.67 


85.91 


19.05 


85.83 


19.42 


88 


89 


87.06 


18.50 


86.97 


18.88 


86.89 


19.26 


86.81 


19.64 


89 


90 
91 


88.03 


18.71 


87.95 
88.93 


19.10 


87.87 


19.48 
19.70 


87.78 


19.86 


90 
91 


89.01 


18.92 


19.31 


88.84 


88.76 


20.08 


92 


89.99 


19.13 


89.91 


19.52 


89.82 


19.91 


89.73 


20.30 


92 


93 


90.97 


19.34 


90.88 


19.73 


90.80 


20.13 


90.71 


20.52 


93 


91 


91.95 


19.54 


91.86 : 19.94 1 


91.77 


20.35 


91.68 


20 . 75 


94 


95 


92.93 19.75 


92.84 20.16 


92.75 


20.56 


92.66 


20.97 


95 


96 


93.90 19.96 


93.81 ! 20.37 


93 . 72 20 . 78 ( 


93.63 


21.19 9fi| 


97 


94.83 20.17 


94.79 1 20.58 1 


94.70 20.99 1 


94.61 ' 21.41 ! 97 


98 


95.86 20.38 


95.77 '20.79 I 


95.68 ' 21.21 


95.58 21.63 1 98 


99 


96. N4 20.. 58 


96.75 121.01 


96.65 21.43 


96.56 i 21.85 1 99 


100 

c 

5 


97.81 20.79 


97.72 i 21.22 


97.63 121.64 


97.53 122.07 |100 


Dep. 1 Lat. 


Dep. 1 Lat. 


Dep. 1 Lat. 


Dep. Lat. | 


78 1 


)ecr. \ 


771 Deg 

i 


77A Deg. 


77il 


3eg. 


Q 



i 



28 



TrwVVFESE TABLE. 





13 Deg. 


134 Deg. 


131 Deg. 


I3.f Deg. 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep, 


~i 


0.97 


0.23 


~1)T97 


0.23 


0.97 


0.23 


0.97 


0,24 


~l 


2 


1.95 


0.45 


1.95 


0.46 


1.95 


0,47 


1.94 


0,48 


2 


3 


2.92 


0.67 


2.92 


0.69 


2.92 


0,70 


2.91 


0,71 


3 


4 


3.90 


0.90 


3.89 


0.92 


3.89 


0,93 


3.89 


0,95 


4 


5 


4.87 


1.12 


4.87 


1.15 


4.86 


1.17 


4.86 


1,19 


5 


6 


5.85 


1.35 


5.84 


1.38 


5.83 


1,40 


5.83 


1,43 


6 


7 


6.82 


1.57 


0.81 


1.60 


6.81 


1,63 


6.80 


1,66 


7 


» 


7.80 


1.80 


7.79 


1.83 


7.78 


1,87 


7.77 


1,90 


8 


y 


8.77 


2.03 


8.76 


2.06 


8.75 


2,10 


8.74 


2,14 


9 


10 

11 


9.74 


2.25 


9.73 


2.29 


9.72 


2,33 


9.71 


2,38 
2,61 


10 
11 


10.72 


2.47 


10.71 


2.52 


10.70 


2,57 


10.68 


12 


11.69 


2.70 


11.68 


2.75 


11.67 


2,80 


11.66 


2.85 


12 


13 


12.67 


2.92 


12.65 


2.98 


12.64 


3,03 


12.63 


3.09 


13 


14 


13.64 


3.I01 


13.63 


3.21 


13.61 


3,27 


13.60 


3.33 


14 


15 


14.62 


3.37; 


14.60 


3.44 


14,59 


3,50 


14.57 


3.57 


15 


16 


15.59 


3.00' 


15.57 


3.67 


15.56 


3,74 


15.54 


3.80 


16 


17 


16.57 


3.821 


10.55 


3.90 


16.53 


3,97 


16.51 


4.04 


17 


IS 


17.54 


4.0.T! 


17.52 


4.13 


17.50 


4,20 


17.48 


4,28 


18 


19 


18.51 


4.27! 


18.49 


4.35 


18.48 


4.44 


18.46 


4,52 


19 


20 

21 


19.49 
20.46 


4.501 

4.72' 


19.47 


4.58 


19.45 


4.67 1 


19.43 


4,75 


20 


20.44 


4.81 


20.42 


4.90 


20.40 


4,99 


21 


22 


21.44 


4.95 


21.41 


5.04 


21.39 


5,14 


21.37 


5,23 


22 


23 


22.41 


5.17 


22.39 


5.27 


22.36 


5,37 


22.34 


5.47 


23 


24 


23.38 


5.40 


23.36 


5.50 


23.34 


5,60 


23.31 


5.70 


24 


26 


24.36 


5.62 


24.33 


5.73 


24.31 


5,84 


24.28 


5.94 


25 


26 


25.33 


5.85 


25.31 


5.96 


25,28 


6.07 


25.25 


6.18 


26 


27 


20.31 


6.07 


26.28 


6.19 


26.25 


6.30 


26.23 


6.42 27l 


28 


27.28 


6.30 


27.25 


6,42 


27.23 


6,. 54 


27.20 


6,66 


28 


29 


28.26 


6.52 


28.23 


6.65 


28,20 


6,77 


28.17 


6.89 


29 


30 
31 


29.23 
30.21 


6.75 


29.20 


6.88 


29,17 


7,00 


29 . 14 


7.13 


30 


6.97 


30.17 


7.11 


30,14 


7,24 


30.11 


7.37 


31 


32 


31.18 


7.20 


31.15 


7.33 


31,12 


7,47 


31.08 


7.61 


32 


33 


32.15 


7.42 


32.12 


7.56 


32,09 


7,70 


32.05 


7.84 


33 


34 


.33.13 


7.65 


33.09 


7.79 


33,06 


7,94 


33,03 


8.08 


34 


35 


34.10 


7.87 


34.07 


8.02 


34,03 


8.17 


34.00 


8.32 


35 


36 


35.08 


8.10 


35.04 


8.25 


35,01 


8.40 


34.97 


8.56 


36 


37 


36.05 


8.32 


36.02 


8.48 


35,98 


8.64 


35.94 


8,79 


37 


38 


37.03 


8.55 


36.99 


8.71 


36,95 


8,87 


36.91 


9,03 


38 


39 


38.00 


8.77 


37.96 


8.94 


37,92 


9.10 


37.88 


9,27 


39 


40 

41 


38.97 


9.09 
9.22 


38.94 


9.17 
9.40 


38,89 


9.34 
9.57 


38.85 


9,51 


40 
41 


39.95 


39.91 


39.87 


39.83 


9,75 


42 


40.92 


9.45 


40.88 


9.63 


40.84 


9.80 


40.80 


9.98 


42 


43 


41.90 


9 67 


41.86 


9.86 


41.81 


10.04 


41.77 


10,22 


43 


44 


42.87 


9.90 


42.83 


19.08 


42.78 


10,27 


42.74 


10,46 


44 


45 


43.85 


10.12 


43.80 


10.31 


43.76 


10.51 


43.71 


10.70 


45 


46 


44.82 


10.35 


44.78 


10.54 


44.73 


10.74 


44.68 


10.93 


46 


47 


45.80 


10.57 


45.75 


10.77 


45,70 


10.97 


45.65 


11.17 


47 


48 


46.77 


10.80 


46.72 


11.00 


46,67 


11.21 


46.62 


11.41 


48 


49 


47.74 


11.02 


47.70 


11.23 


47.65 


11.44 


47.60 


11,65 


49 


50 


48.72 


11.25 


48.67 


11.46 


48,62 


11.67 


48.57 


11,88 


^0 


1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat, 


1 

5 


77 


Deg. 


761 Deg. 


761 


Deg. 


76i Deg. 



TRAVERSE TABLE. 



29 



51 


13 Deg. 


13i Deg. 


13-i Deg, 


131 Deo. 


s 
? 
51 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep, 


Lat. 


Dep. 


49.69 


11,47 


49.64 


11.69 


49,. 59 


11.91 


49.54 


12.12 


52 


50.67 


11,70 


50.62 


11.92 


50.. 56 


12.14 


.50.61 


12.36 


52 


53 


51.64 


11.92 


51.59 


12.15 


51.54 


12.37 


51.48 


12.60 


53 


54 


52.62 


12.15 


.52.66 


12.38 


.52.51 


12.61 


52.45 


12.84 


54 


55 


53.. 59 


12.37 


53.. 54 


12.61 


63.48 


12.84 


.53.42 


13.07 


55 


56 


54.56 1 12.60 


54.51 


12.84 


54.45 


13.07 


54.40 


13.31 


5C 


57 


55.541 12.82 


55.48 


13.06 


.55.43 


13.31 


.55.37 


13., 55 


57 


68 


50.51 


13.05 


56.46 


13.29 


.56.40 


13.. 54 


56 34 


13.79 


58 


59 


57.49 


13.27 


.57.43 


13.52 


57.37 


13.77 


67.31 


14.02 


59 


60 


58.46 


13. .50 


58.40 


13.75 


58.34 


14.01 


.58.28 


14.26 


60 


"61 


59.44 


13.72 


59.38 


13.98 


59.31 


"14.24 


59.25 


14.. 50 


61 


62 


60.41 


13.95 


60.35 


14.21 


60.29 


14.47 


60.22 


14.74 


62 


63 


61.39 


14.17 


61.32 


14.44 


61.26 


14.71 


61.19 


14.97 


63 


f;4 


62.36 


14.40 


62.. 30 


14.67 


62.23 


14.94 


62.17 


15.21 


64 


65 


63.33 


14.62 


63.27 


14.90 


63.20 


15.17 


63.14 


15.45 


65 


66 


64.31 


14.85 


64.24 


15.13 


64,18 


15.41 


64,11 


15.69 


66 


67 


65. 2S 


15.07 


65.22 


15.36 


65,15 


15.64 


65,08 


15.93 


67 


68 


6f..26 


15.30 


66.19 


15.59 


66,12 


15,87 


€6,05 


16.16 


68 


69 


67.23 


15.52 


67.16 


15.81 


67,09 


16,11 


67,02 


16.40 


69 


70 
71 


68,21 


15,75 


68.14 


16,04 
16.27 


68.07 


16.34 
16.57 
16.81 
17.04 


67,99 


16.64 


70 

"71 


69.18 


15.97 


69.11 


69.04 


68,97 


16.88 


72 


70.15 


16.20 


70.08 


16. .50 


70.01 


69.94 


17,11 


72 


73 


71.13 


16,42 


71.06 


16.73 


70.98 


70.91 


17.35 


73 


74 


72.10 


16.65 


72.03 


16.96 


71.96 


17.28 


71.88 


17.59 


74 


,75 


73.08 


16.87 


73.00 


17.19 


72.93 


17,50 


72.85 


17.83 


75 


76 


74.05 


17.10 


73.98 


17.42 


73.90 


17,74 


73.82 


18.06 


76 


77 


75.03 


17.32 


74.95 


17.65 


74.87 


17,98 


74.79 


18.30 


77 


78 


70.00 


17.55 


75.92 


17.88 


75,84 


18,21 


75.76 


18.. 54 


78 


79 


70.98 


17.77 


76.90 


18.11 


76.82 


18,44 


76.74 


18.78 


79 


80 
81 


77.95 


18.00 


77,87 
78.84 


18.34 
18. ".57' 


77.79 
78.76 


18,68 


77.71 
78,68 


19.01 
19.25 


80 
81 


78.92 


18.22 


18,91 


82 


79.90 


18.45 


79.82 


18.79 


79.73 


19.14 


79.65 


19.49 


82 


83 


80.87 


18.67 


80.79 


19.02 


80.71 


19.38 


80.62 


19.73 


83 


84 


81.85 


18.90 


81.76 


19.25 1 


81.68 


19.61 


81.. 59 


19.97 


84 


85 


82 . 82 


19.12 


82.74 


19.48 ' 


82.65 


19.84 


82.. 56 


20.20 


85 


86 


83.80 


19.35 


83.71 


19.71 


83.62 


20-08 


83.54 


20.44 


86 


87 


81.77 


19.57 


84.68 


19.94; 


84.60 


20.31 


84.51 


20.68 


87 


88 


85.74 


19,80 


85.66 


20.17 


85 . 57 


20.54 


85.48 


20.92 


88 


89 


86.72 


20.02 


86.63 


20.40 i 


86.. 54 


20.78 


86.45 


21.15 


89 


90 
91 


87.69 
88.67 


20.25 


87.60 
88.58 


20,63 
20.86 ' 


87.51 
88.49 


21.01 
21.24 


87.42 
88.39 


21.39 
21.63 


90 
91 


20.47 


92 


89. P4 


20.70 


89.55 


21.09 


89.46 


21.48 


89.36 


21.87 


92 


93 


90.62 


20.92 


90. .52 21.32 


90.43 


21.71 


90.33 


22.10 


93 


94 


91.59 


21.15 


91.. 50 21.. 54 


91.40 


21.94' 


91.31 


22.34 


94 


9r. 


92.. 57 


21,37 


92.47 


21.77 


92..38i22.18| 


92.28 


22.58 


95 


96 


93 . 54 


21.60 


93.44 


22.00 


93..35 122.41 1 


93.25 


22.82 


96 


97 


94.51 


21.82 


94.42 


22.23 ; 


94.32 


22.64 1 


94.22 


23.06 


97 


98 


95.49 


■>.2.05 


95.39 


22.46 


95.29 


22.88 1 


95.19 


23.29 


98 


99 


96.46 


22.27 


96.36 


22.69 


96.26 


23.11 


96.16 


23.53 


99 


100 

8 

c 

at 
.2 
Q 


97.44 


22.50 


97.34 22,92 


97.24 


23.34 


97.13 


23.77 


100 


Dcp. 


-•i 


Dep, 


T.rj 


Dep. 


Lat. 

1 


Dep. 


Lat. 


5 


77 Deg. 


76} Deg. j 


76i Deg, 


76} Deg. 



21 



30 



TRAVERSE TABLE. 





.Oe. [ 


14iDeg. 


Uk 


Deg. 


1 
141 Deg. 


3 


Lat.| 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


~o79T' 


~0"."2T 


0.97 


0.25 


~'o:w 


0.25 


0.97 


0.25 


~~i 


2 


1.94 


0.48 


1.94 


0.49 


1.94 


0.50 


1.93 


0.51 


2 


3 


2.91 


0.73 


2.91 


0.74 


2.90 


0.75 


2.90 


0,76 


3 


, 4 


3.88 


0.97 


3.88 


0.98 


3.87 


1.00 


3.87 


1,02 


4 


5 


4.85 


1.21 


4.85 


1.23 


4.84 


1.25 


4.84 


1,27 


5 


6 


5.82 


1.45 


5.82 


1.48 


5.81 


1.50 


5.80 


1.53 


6 


7 


6.79 


1.69 


6.78 


1 72 


6.78 


1.75 


6.77 


1.78 


7 


8 


7.76 


1.94 


7.75 


1.97 


7.75 


2.00 


7.74 


2.04 


8 


9 


8.73 


2.18 


8.72 


2.22 


8.71 


2.25 


8.70 


2.29 


9 


10 
11 


9.70 
10.67 


2.42 
2.66 


9.69 


2.46 
2.71 


9.68 


2.50 

2.75 1 


9.67 


2.55 

2.80 


10 
11 


10.66 


10.65 


10.64 


12 


11 . 04 


2.90 


11.03 


2.95 


11.62 


3.00 


11.60 


3.06 


12 


13 


12.61 


3.15 


12.60 


3.20 


12.59 


3.25 


12.57 


3.3) 


13 


14 


13.58 


3.39 


13.57 


3.45 


13.55 


3.51 


13.. 54 


3.. 56 


14 


15 


14.55 


3.63 


14.54 


3.69 


14.. 52 


3.76 


14.51 


3.82 


15 


16 


15.52 


3.87 


15.51 


3.94 


15.49 


4.01 


15.47 


4.07 


16 


17 


16.50 


4.11 


16.43 


4.18 


16.46 


4.26 


16.44 


4.33 


17 


18 


17.47 


4.35 


17.45 


4.43 


17.43 


4.51 


17.41 


4 . 58 


18 


19 


18.44 


4.60 


18.42 


4.63 


18.39 


4.76 


18.37 


4.34 


19 


20 
21 


19.,41 


4.84 


19.38 


4.92 


19.36 


5.01 
5.26 


19.34 


5.09 


20 
21 


20.38 


5.08 


20.35 


5.17 


20.31 


5,. 35 


22 


21.35 


5.32 


21.32 


5.42 


21.30 


5.51 


21.28 


5.60 


22 


23 


22.32 


5.56 1122.29 
5.81 ,23.26 


5.66 


22.27 


5.76 


22 . 24 


5.86 


23 


2t 


23.99 


5.91 


23.24 


6.01 


23.21 


6,li 


24 


25 


24,26 


6.05 


24.23 


6.15 


24.20 


6.26 


24.18 


6.37 


25 


26 


25.23 


6.29 


25.20 


6.40 


25.17 


6.51 


25.14 


6,62 


28 


27 


26.20 


6.53 


26.17 


6.65 


26.14 


6.76 


26.11 


6,87 


27 


28 


27.17 


6.77 


27.14 


6.89 


27.11 


7.01 


27.08 


7,13 


23 


29 


2S.14 


7.02 


28.11 


7.14 


28.08 


7.26 


28.04 


7,33 


29 


30 
31 


29.11 
30.08 


7.26 
7.50 


29. OS 


7.38 


29.04 


7.51 


29.01 


7.64 

7.'8y 


30 
31 


30.05 


7.63 


30.01 


7.76 


29.93 


32 


31.05 


7.74 


31.02 


7.88 


30.98 


8.01 


30.95 


8.15 


32 


33 


32.02 


7.98 


31.93 


8.12 


31.95 


8.26 


31.91 


8.40 


33 


34 


32.99 


8.23 


32.95 


8.37 


32 . 92 


8.51 


32.83 


8. 60 


34 


35 


33.96 


8.47 


.33 . 92 


8.62 


33.89 


8.76 


33.85 


8.91 


35 


36 


.34.93 


8.71 


34.89 


8.86 


34.85 


9.01 


34.81 


9.17 


36 


37 


35.90 


8.95 


35.86 


9.11 


35.82 


9.26 


.35.78 


9.42 


37 


38 


36.87 


9.19 


36.83 


9.35 


36.79 


9.51 


36.75 


9.67 


38 


39 


37.84 


9.44 


37.80 


9.60 


37.76 


9.76 


37.71 


9.93 


39 


40 


3S.81 


9.68 


33.77 


9.85 


38.73 


10.02 


38.63 


10.18 


40 


41 


33.78 


9.92 


39.74 


10.09 


39.69 


10.27 


39. "65 


10.44 


41 


42 


4'J.75 


10.16 


40.71 


10.34 


40.66 


10.52 


40.62 


10.69 


42 


43 


41.72 


10.40 


41.68 


10.58 


41.63 


10.77 


41.. 58 


10.95 


43 


44 


42.69 


10.64 


42.65 


10.83 


42.60 


11.02 


42.-55 


11.20 


44 


45 


i 43.66 


10.89 


43.62 


11.08 


43.57 


11.27 


43.52 


11.46 


45 


46 


144.63 


11.13 


44.58 


11.32 


44.53 


11.52 


44.48 


11.71 


46 


47 


45.60 


11.37 


45.55 


11.57 


45.. 50 


11.77 


45.45 


11.97 


47 


48 


46 . 57 


11.61 


46 . 52 


11.82 


48.47 


12.02 


46.42 


12.22 


48 


49 


47.54 


11.85 


I 47.49 


12.06 


47.44 


12.27 


47.39 


12.48 


49 


50 

i 

i 

.2 

Q 


,48.51 


12.10 


48.46 


12.31 


48.41 


12.52 


48.35 


12.73 


50 


Dep, 


1 Lat. 


Dep. 


iLa.. 
Dag. 


Dep. 


Lat. 


Dep. 


Lat. 


1 

3 


76 


Deg. 


^H 


Deg. 


15\ 


Deg. 



TRAVERSE TABLE. 



31 



1' 

51 


14 Deg. 


14i Deg. 


141 Deg. 


141 Deg. 


1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 

49.38 


Dep. 


Lat. 


Dep. 

T2T98 


49.49 


12,34 


49.43 


12.55 


12.77 


49.32 


52 


50.46 


12.58 


50.40 


12.80 


50.34 


13.02 


.50,29 


13.24 


52 


53 


51.43 


12.82 


51.37 


13.05 


51.31 


13.27 


51.25 


13.49 


53 


54 


52.40 


13.06 


52.34 


13.29 


52.28 


13. ,52 


52,22 


13.75 


54 


55 


53.37 


13.31 


53.31 


13.54 


53.25 


13,77 


.53.19 


14,00 


55 


56 


54.34 


13.55 


54.28 


13.78 


54.22 


14,02 


.54.15 


14,26 1 561 


57 


55.31 


13.79 


.55.25 


14.03 


.55.18 


14.27 


.55.12 ! 14.51 i 57| 


5S 


56.28 


14.03 


.56.22 


14.28 


56.15 


14. .52 


56.09 


14,77 581 


59 


57.25 


14.27 


57.18 


14.52 


57.12 


14.77 


57.06 


15,02 ! 591 


60 
61 


58.22 


14.52 


.58.15 


14.77 
16,02 


.58.09 


15.02 


.58.02 
58.99 


15,28 


60 
61 


69.19 


14.76 


59.12 


59 . 06 


15.27 


15,. 53 


62 


60.16 


15.00 


60.09 


15,26 


60.03 


15.52 


.59 . 90 


15.79 


62 


63 


61.13 


15.24 


61.06 


15.51 


60.99 


15.77 


60.92 


16.04 


63 


64 


62.10 


15.48 


62.03 


15.75 


61.96 


16.02 


61.89 


16.29 


64 


65 


63.07 


15.72 


63.00 


16,00 


62 . 93 


16.27 


62.86 


16.. 55 


65 


66 


64.04 


15.97 


63.97 


16.25 


63.90 


16.53 


63.83 


16.80 


66 


67 


65.01 


16.21 


64.94 


16.49 


64.87 


16.78 


64.79 


17.06 


67 


68 


65.98 


16.45 


65.91 


16.74 


65.83 


17.03 


65.76 


17.31 


68 


CO 


66.95 


16.09 


66.88 


16,98 


66.80 


17,28 


66.73 


17.57 


69 


70 
71 


67.92 


16.93 


67.85 


17.23 


67.77 


17.53 
17.78 


67.69 
68.66 


17.82 


70 


68.89 


17.18 


68.82 


17.48 


68 . 74 


18.03 


71 


72 


69.86 


17.42 


69.78 


17.72 


69.71 


18.03 


69.63 


18.33 72 


73 


70.83 


17.66 


70.75 


17.97 


70.67 


18.28 


70.. 59 


18.59 73 


74 


71.80 


17.90 


71.72 


18.22 


71.64 


18.. 53 


71.56 


18.84 74 


75 


72 77 


18.14 


72.69 


18.46 


72.61 


18.78 


72., 53 


19.10 75 


76 


V3 74 


18.39 


73.66 


18.71 


73.58 


19.03 


73,. 50 


19., 35 


76 


77 


74.71 


18.63 


74.63 


18.95 


74.. 55 


19.28 


74.46 


19.60 


77 


78 


75.68 


18.87 


73,60 


19.20 


75.52 


19.. 53 


75.43 


19.86 


78 


79 


76.65 


19.11 


76.57 


19.45 


76.48 


19.78 


76.40 


20.11 


79 


80 
81 


77.62 
78.. 59 


19.35 


77.. 54 


19.69 


77.45 


20.03 


77.. 36 
78.33 


20.37 
20.62 


80 
81 


19.60 


78.51 


19.94 


78.42 


20,28 


82 


79.56 


19.84 


79.48 


20,18 


79.. 39 


20,. ^3 


79.30 


20.88 


82 


83 


80.. 53 


20.08 


80.45 


20,43 


80.36 


20,78 


80.20 


21.13 


83 


84 


81.50 


20.32 


81.42 


20,68 


81.32 


21,03 


81.23 


21.39 


84 


85 


82.48 


20.56 


82.. 38 


20,92 


82.29 


21.28 


82.20 


21,64 


85 


86 


83.45 


20.81 


83.35 


21,17 


83.26 


21.53 


83.17 


21.90 


86 


87 


84.42 


21.05 


84.32 


21.42 


84.23 


21.78 


84.13 


22.15 


87 


88 


85.. 39 


21.29 


85.29 


21.66 


85.20 


22.03 


85.10 


22.41 


88 


89 


86.36 


21.53 


86.26 


21.91 


86.17 


22.28 


86.07 


22.66 


89 


90 
91 


87.33 


21.77 
22.01 


87.23 


22.15 
22.40 


87.13 


22.. 53 


87.03 


22,91 


90 
91 


88.30 


88.20 


88.10 


22.78 


88.00 


23,17 


92 


89.27 


22.26 


89.17 


22.65 


89.07 


23.04 


88.97 


23,42 42 


93 


90.24 


22.. 50 


90.14 


22.89 


90.04 


23.29 


89.94 


23,68 1 93 


94 


91.21 


22.74 


91.11 


23.14 


91.01 


23. .54 


90.90 


23.93 1 94 


95 


92.18 


22.98 


92.08 


23.38 


91.97 


23.79 


91.87 


24.19 1 95 


96 


93.15 


23.22 


93.05 


23-63 


92.94 


24.04 


92.84 


24.44 1 96 


97 


94.12 


23.47 


94,02 


23.88 


93.91 


24.29 


93.80 


24.70 97 


98 


95.09 


23.71 


94.98 


24.12 


94.88 


24.. 54 


94,77 


24.95 i 98 


99 96.06 


23 95 


95.95 


24.37 


95.85 


24.79 


95,74 


25.2! ' 99 


100 


97.03 


24.19 


96.92 


24.62! 


96.81 


25.04 


96.70 


25.46 ,190 


s 

c 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. , 


c 


Q 


76 Deg. 


75| Deg 


75^ Deg. 


75iDeg 





TRAVERSE TABLE. 





15 Deg. 


15^ Deg. 


15i 


Deg. 


15i Deg. 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.97 


0.26 


0.96 


0.26 


0.96 


0.27 


0.96 


0.27 


1 


2 


1.93 


0.52 


1.93 


0..53 


1.93 


0.53 


1.92 


0.54 


2 


3 


2.90 


0,78 


2.89 


0.79 


2.89 


0.80 


2.89 


0.81 


3 


4 


3.86 


1.04 


3.86 


1.05 


3.85 


1.07 


3.85 


1.09 


4 


5 


4.83 


1.29 


4.82 


1.32 


4.82 


1.34 


4.81 


1.36 


5 


6 


5.80 


1.55 


5.79 


1.58 


5.78 


1.60 


5.77 


1.63 


6 


7 


0.76 


1.81 


6.75 


1.84 


6.75 


1.87 


6.74 


1.90 


7 


8 


7.73 


2.07 


7.72 


2.10 


7.71 


2.14 


7.70 


2.17 


8 


9 


8.69 


2.33 


8.68 


2.37 


8.67 


2.41 


8.66 


2.44 


9 


10 


9.60 


2.59 


9.65 


2.63 


9.64 


2.67 


9.62 


2.71 
2". 99 


10 
11 


11 


10.63 


2.85 


10.61 


2.89 


10.60 


2.94 


10.59 


12 


11.59 


3.11 


11.58 


3.16 


1 1 . 56 


3.21 


11, .55 


3.26 


12 


13 


12.56 


3.36 


12.54 


3.42 


12.53 


3.47 


12,51 


3.53 


13 


14 


13.52 


3.62 


13.51 


3.68 


13.49 


3.74 


13.47 


3.80 


14 


15 


14.49 


3.88 


14.47 


3.95 


14.45 


4.01 


14.44 


4.07 


15 


16 


15.45 


4.14 


15.44 


4.21 


15.42 


4.28 


15.40 


4.34 


16 


17 


16.42 


4.40 


16.40 


4.47 


16.38 


4.54 


16.36 


4.61 


17 


18 


17.39 


4.06 


17.37 


4.73 


17.35 


4.81 


17.32 


4.89 


18 


19 


18.35 


4.92 


18.33 


5.00 


18.31 


5.08 


18.29 


5.16 


19 


20 


19.32 


5.18 
5.44 


19.30 
20.26 


5.26 


19.27 


5.34 


19.25 


5.43 

5. "70 


20 

21 


21 


20.28 


5.52 


20.24 


5.61 j 


20.21 


22 


21.25 


5.69 


21.23 


5.79 


21.20 


5.88 1 


21.17 


5.97 


22 


23 


22.22 


5.95 


22.19 


6.05 


22.16 


6.151 


22.14 


6.24 


23 


24 


23.18 


6.21 


23.15 


0.31 


23.13 


6.41 


23.10 


6.51 


24 


2o 


24.15 


6.47 


24.12 


6.. 58 


24.09 


6.68' 


24.06 


6.79 


25 


26 


25.11 


6.73 


25.08 


6.84 


25.05 


6.95 1 


25.02 


7.06 


26 


27 126,08 


6.99 


26.05 


7.10 


26.02 


7.22 


25.99 


7.33 


27 


28 27.05 


7.25 


27.01 


7.36 


26.98 


7.48 


26.95 


7.60 


28 


29 


28.01 


7.51 


27.98 


7.63 


27.95 


7.75 


27.91 


7.87 


29 


30 
31 


28.98 


7.76 


28 . 94 


7.89 


28 . 9 1 


8.02 


28.87 


8.14 

8.41 


30 
31" 


29.94 


8.02 


29.91 


8.15 


29.87 


8.28 


29.84 


32 


30.91 


8.28 


30.87 


•8.42 


30. H4 


8.55 


30.80 


8.69 


32 


33 


31.88 


8.54 


31.84 


8.68 


31.80 


8.82 


31.76 


8.90 


33 


34 


32.84 


8.80 


32 . 80 


8.94 


32.76 


9.09 


32.72 


9.23 


34 


35 


33 . 8 1 


9.06 


33.77 


9.21 


33.73 


9.35 


33.69 


9.5'1 


35 


36 


34.77 


9.32 


34 . 73 


9.47 


34.69 


9.62 


31 . 65 


9.77 


36 


37 


35.74 


9.. 58 


35 . 70 


9.73 


35 . 65 


9.89 


35.61 


10.04 


37 


38 


36.71 


9.84 


36.66 


10.00 


36.62 


10.16 


36.. 57 


10.31 


38 


39 


37.67 


10.09 


37.63 


10.26 


37 . 58 


10.42 


37.. 54 


10.59 


39 


40 


33.64 


10.35 


38.59 


1 10. .52 


3S.55 


10.69 

To:96- 


3S . 50 
3;».46 


10.86 
11.13 


10 
41 


41 


39.60 


1 10.61 


39.56 


1 10.78 


39 . 5 1 


42 


40.57 


1 10.87 


40.. 52 


11.05 


40.47 


11.22 


40.42 


11.40 


42 


43 


41.53 


j 11.13 


41.49 


11.31 


41.44 


11.49 


41.39 


11.67 


43 


44 


42.50 


1 11.39 


42.45 


11.57 


42.40 


11.76 


42.35 


11.94 


44 


45 


43.47 


1 11.65 


43.42 


11.84 


43.36 


12.03 


143.31 


12.21 


45 


46 


44.43 


11.91 


44.38 


12.10 


44.33 


12.29 


44.27 


12.49 


46 


47 1 15.40 


' 12.16 


145.35 


12.30 


45.29 


12.56 


45.24 


12.76 


47 


48 


46.36 


i 12.42 


46.31 


12.63 


46.25 


12.83 


46.20 


13.03 


48 


49 


47.33 


1 12.68 i 47.27 


12.89 


47.22 


13.09 


47.16 


13.30 


49 


50 


48.30 


j 12.94 : 48.24 


13.15 


48.18 


13.36 
Lat, 


48.12 


13.57 


50 

i 
s 


s 

c 
.2 


Dep. 


1 Lat. jl Dep. 


1 Lat. 


Dep. 


Dep. 


Lat. 


75 


Deg. 74! 


Deg. 


74. 


Deg. 


74i Deg. 



TRAVERSE TjVBLE. 



33 



2 

5. 
1 
5T 


15 Dcg. 


15i Deg. 


15i Deg. 


151 Deg. 


i 

5j 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


49.26 


T3726" 


49.20 


13.41 


49.15 


13.63 


49.09 


13.84 


52 


50.23 


13.46 


50. J7 


13.68 


50 . 1 1 


13.90 


.50.05 


14.11 


52 


53 


51.19 


13.72 


51.13 


13.94 


51.07 


14.16 


51.01 


14.39 


63 


54 


.52.16 


13.98 


52.10 


14.20 


.52.04 


14.43 


51.97 


14.60 


54 


55 


53,13 14.241 


53.06 


14.47 


.53.00 


14.70 


.52.94 


14.93 


■ 65 


56 


54.09 


14.49 


54.03 


14.73 


53.96 


14.97 


63.90 i 15.20 


56 


57 


55.06 


14.75 


54.99 


14.99 


54.93 


15.23 


.54.86 15.47 


57 


58 


56.02 


15.01 


55.96 


15.26 


55.89 


15.. 50 


.55.82 15.74 


58 


59 


.56.99 


15.27 


56.92 


15.52 


56.85 


15.77 


56.78 1 16.01 


59 


60 
61 


57.96 


15.53 


57.89 


15.78 


57.82 
58 . 78 


16.03! 
16.30 i 


57.75 1 16.29 


60 

"61 


58.92 


15.79 


58.85 


16.04 


58.71 i 16. .56 


62 


59.89 


16.05 


59.82 


16.31 


59 . 75 


16.57 


59.67 16.83 


62 


63 


60.85 


16.31 


60.78 


16.57 


60,71 


16.84 


60.63 I 17.10 


63 


64 


61.82 


16.56 


61.75 


16.83 


61.67 


17.10 


CI. 60 ! 17.37 


64 


65 


62.79 


16.82 


62,71 


17.10 


62.64 


17.37 


62.. 56 17.64 


65 


66 


63.75 


17.08 


63.68 


17. 3S 


63.60 


17.64 


03.52 


17.92 


66 


67 


64.72 


17.34 


64.64 


17.62 


64.56 


17.90 


64. 4S 


18.19 


67 


63 


65.68 


17.60 


65.61 


17.89 


65.53 


18.17 


65.45 


18.40 


68 


69 


66.65 


17.86 


66.57 


18.15 


66.49 


18.44 


66.41 


18.73 


69 


70 

71 


67.61 


18.12 


67.54 


18.41 


67.45 


18.71 


67.37 


19.00 


70 
71 


68.58 


18.38 


68.. 50 


18.68 


68.42 


18.97 


68.33 19.27 


72 


69.55 


18.63 


09.46 


18.94 


69.38 


19.24 


69.30 1 19.54 


72 


73 


70.51 


18.89 


70.43 


19.20 


70.35 


19.51 


70.26 


19.82 


73 


74 


71.48 


19.15 


71.39 


19.46 


71.31 


19.78 


71.22 


20.09 


74 


75 


72.44 


19.41 


72.36 


19.73 


72.27 


20.04 


72.18 


20..% 


75 


76 


73.41 


19.67 


73.32 


19.99 


73 . 24 


20.31 


73,15 


20.63 


76 


77 


74.38 


19.93 


74.29 


20.25 


74.20 


20.58 


74.11 


20.90 


77 


78 


75.34 


20.19 


75.25 


20.. 52 


75.16 


20.84 


75.07 


21.17 


78 


79 


76.31 


20.45 


76.22 


20.78 


76.13 


21.11 


76.03 


21.44 


79 


80 
81 


77.27 


20.71 


77.18 


21.04 


77.09 


21.38 


77.00 


21.72 


80 
81 


78.24 


20.96 


78.15 


21.31 


78.05 


21.65 


77.96 


21.99 


82 


79.21 


21.22 


79.11 


21.. 57 


79.02 


21.91 


78.92 


22.26 


82 


83 


80.17 


21.48 


80.08 


21.83 


79.98 


22.18 


79.88 


22.53 


83 


84 


81.14 


21.74 


81.04 


22.09 


80.94 


22.45 


80.85 


22.80 


84 


85 


82.10 


22.00 


82.01 


22.36 


81.91 


22.72 


81.81 


23.07 


85 


86 


83.07 


22.26 


82.97 


22.62 


82.87 


22.98 


82.77 


23.34 


86 


87 


84.04 


22.52 


83.94 


22.88 


83.84 


23.25 


83.73 


23.62 


87 


88 


85.00 


22.78 


84.90 


23.15 


84.80 


23.. 52 


84.70 


23.89 


88 


89 


85.97 


23.03 


85.87 


23.41 


85.76 


23.78 


85.66 


24.16 


89 


91 


86.93 


23.29 


86.83 


23.67 


86.73 


24.05 


86.62 


24.43 


90 
91 


87.90 


23.55 


87.80 


23.94 


87.69 


24.32 


"87758 


24.70 


92 


88.87 


23.81 


88.76 


24.20 


88 . 65 


24.59 


188.55 


24.97 


92 


93 


89.83 


24.07 


89.73 


24.46 


89.62 


24.85 


89.51 


25.24 


93 


94 


90.80 


24.33 


90.69 


24.72 


90.58 


25.12 


90.47 


25.52 


94 


95 


91.76 


24.59 


91.65 


24.99 


91.54 


25.39 


91.43 


25.79 


95 


96 


92 73 


24.85 


92.62 1 25.25 


92.51 


25.65 


92.40 126.06 


96 


97 


93.69 


25.11 


93.58 


25.51 


93.47 


25.92 


93.36 


26.. 33 


97 


98 


94.66 


25.36 


94.55 


25.78 


94.44 


26.19 


94.32 


26.60 


98 


99 


95.63 


25.62 


95.51 


26.04 


95.40 


26.46 


95.28 


26.37 


99 


100 

i 

i 


96.59 
Dep, 


25.88 


36.48 


26.30 


96.36 


26.72 


96.25 


27.14 


100 

1 ^ 


Lat. 


Dep. 


Lat. 


Dep. 


Lat, 


Dep. 


Lat. 


75 Deg. 


741 Deg. 


74^ Deg. 


74iDcg. 



34 



TRAVEKSE TABLE. 



1 


16 Deg. 


164 Deg. 


161 Deg. 


161 Deg. 


3 
? 


L... 


Dep. 


Lat. 


Dep. 


Lat. 


Dep, 


Lat. 


Dep. 


0.96 


0.28 


0.96 


0.28 


0.96 


~0 28" 


0.96 


0.29 


2 


1 93 


0.55 


1.92 


0.56 


1.92 


6.57 


1.92 


0.58 


2 


3 


2.88 


0.83 


2.88 


0.84 


2.88 


0.85 


2.87 


0.85 


3 


4 


3.85 


1.10 


3.84 


1.12 


3.84 


1.14 


3.83 


1.15 


4 


5 


4.81 


1.38 


4.80 


1.40 


4.79 


1.42 


4.79 


1.44 


5 


6 


5.77 


1.65 


5.76 


1.68 


5.75 


1.70 


5.75 


1.73 


6 


7 


6.73 


1.93 


0.72 


1.96 


6.71 


1.99 


e.70 


2.02 


7 


8 


7.69 


2.21 


7.68 


2.24 


7.07 


2.27 


7.66 


2.31 


8 


9 


8.65 


2.48 


8.64 


2.. 52 


8.63 


2.. 56 


8.62 


2 . 59 


9 


10 
11 


9.01 


2.76 


9.60 


2.80 


9.. 59 


2.84 


9.58 


2.88 


10 


10.57 


3.03 


10., 56 


3.08 


10.55 


3.12 


10.. 53 


3.171 ll! 


12 


11.54 


3.31 


11.52 


3.36 


11.51 


3.41 


11.49 


3.46 


12 


13 


12.. 50 


3.58 


12.48 


3.64 


12.46 


3.69 


12.45 


3.75 


13 


14 


13.40 


3.86 


13.44 


3.92 


13.42 


3.98 


13.41 


4.03 


14 


15 


14.42 


4.13 


14.40 


4.20 


M..38 


4.26 


14.36 


4.32 


15 


16 


15.38 


4.41 


15.36 


4.48 


15.34 


4.54 


15.32 


4.61 


16 


17 


16.34 


4.69 


16.32 


4.76 


16.30 


4.83 


16.28 


4.90 


17 


18 


17.30 


4.96 


17.28 


5.04 


17.26 


5.11 


17.24 


5.19 18| 


19 


18.26 


5.241 


18.24 


5.32 


18.22 


5.40 


18.19 


5.48 


19 


20 


19.23 


5.51 


19.20 


5.60 


19.18 


5.68 


19.15 


5.76 
6.05 


20 
21 


21 


20.19 


5.79 


20.16 


5.88 


20.14 


5.96 


20.11 


22 


21.15 


6.06 


21.12 


6.16 


21.09 


6.25 


21.07 


6.34 


22 


23 


22 . 1 1 


6.34 


22.08 


6.44 


22.05 


6.53 


22.02 


6.63 


23 


24 


23.07 


6.62 


23.04 


6.72 


23.01 


6.82 


22.98 


6.92 


24 


25 


24.03 


6.89 


24.00 


7.00 


23.97 


7.10 


23.94 


7.20 


25 


26 


24.99 


7.17 


24.96 


7.28 


24.93 


7.38 


24.90 


7.49 


26 


27 


25.95 


7.44 


25.92 


7.. 56 


25.89 


7.67 


25.85 


7.78 


27 


28 


20.92 


7.72 


20.88 


7.84 


26.85 


7.95 


20.81 


8.07 


28 


29 


27.83 


7.99 


27.84 


8.11 


27.81 


8.24 


27.77 


8.36 


29 


30 


28.84 


8.27 


28.80 


8.39 


28.76 


8.52 


28.73 


8.65 


30 


31 


29.80 


8.. 54 


29 . 76 


8.67 


29.72 


8.80 


29.68 


•8.93 


31 


32 


30.76 


8.82 


.30.72 


8.95 


30.68 


9.09 


30.64 


9.22 


32 


33 


31.72 


9.10 


31.68 


9.23 


31.64 


9.37 


31.60 


9.51 


33 


34 


32.68 


9.37 


32.64 


9.51 


32.60 


9.66 


32.56 


9.80 


34 


35 


33.64 


9.65 


33.60 


9.79 


33.56 


9.94 


33.51 


10.09 


35 


36 


34.61 


9.92 


34.56 


10.07 


34.52 


10.22 


34.47 


10.38 


36 


37 


35.57 


10.20 


35., 52 


10.35 


35.48 


10.51 


35.43 


10.66 


37 


38 


36.53 


10.47. 


36.48 


10.63 


36.44 


10.79 


36.39 


10.95 


38 


39 


37.49 


10.75 


37.44 


10.91 


37.39 


11.08 


37.35 


n.24 


39 


40 
41 


38 . 45 


11.03 


38.40 


11.19 


38.35 
39.31 


11.36 


38.30 


11. .53 


40 
41 


39.41 


11.30 


' 39.36 


11.47 


1 1 . 64 


39.26 


11.82 


42 


40.37 


1 1 . 58 


40.32 


11.75 


40.27 


11.93 


40.22 


12.10 


42 


43 


41.33 


11.85 


41.28 


12.03 


41.23 


12.31 


41.18 


12. ,39 


43 


44 


42.30 


12.13 


42.24 


12.31 


42.19 


12., 50 


42.13 


12.68 


44 


45 


43.26 


12.40 


43.20 


12.59 


43.15 


12.78 


43.09 


12.97 


45 


46 


44.22 


12.68 


44.16 


12.87 


44.11 


13.06 


44.05 


13.26 


46 


47 


45.18 


12.95 


45.12 


13.15 


45.00 


13.35 


45.01 


13.55 


47 


48 


46.14 


13.23 


46.08 


13.43 


46.02 


13.63 


45,96 


13.83 


48 


49 


47.10 


13.51 


47.04 


13.71 


46.98 


13.92 


46.92 


14.12 


49 


50 


48.08 


13.78 


48.00 


13.99 


47.94 


14.20 


47.88 


14.41 


50 


T 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


74 


Deg. 


731 Deg. 


731 


Deg. 


73i Deg. 


s 



TRA.VERSE TABLE. 



35 



o 

3 
? 

51 


16 Deg. 


WiDeg. 


16 i Dsg 


161 Deg. 


P 

.51 


^LaT' 


Dop. 


LatT' 


Dep. 


Lat. 


Dep. 


Lat. 

48T84 


Dep. 

14". 70 


49.02 


14.06 


48.96 


14.27 


48.90 


T4r4T 


52 


49.99 


14.33 


49.92 


14.. 55 


49.86 


14.77 


49.79 


14.99 


5-Z 


53 


50.95 


14.61 


50.88 


14.83 


.50.82 


15.05 1 


50 . 75 


16.27 


53 


64 


51.91 


14.88 


51.84 


15.11 


51.78 


15.34! 


51.71 


15.56 


5.i 


55 


52.87 


15.16 


.52.80 


15.39 


52.74 


15.62' 


52.67 


15.85 


5.n 


56 


.=^3.83 15.44 


.53.76 


15.67 


.53.69 


15.90 


63.62 


16.14 


6i:i 


57 


54.79 15.71 


.54.72 


15.95 


.54.65 


16.19 


.54.. 58 


16.43 




58 


,55.75 15.99 


55.68 


16.23 


.55.61 


16.47 


55.. 54 


16.72 


,58 


59 


56.71 


16.26 


.56.64 


16.51 


56.57 


16.76 


66 . .50 


17.00 


59 


60 


57.68 


16.54 


57.60 


16.79 


57.-53 


17.04 


57.45 


17.29 


60 


61 


.58.64 


16.81 


58.56 


17.07 


.58.49 


17.32 


58.41 


17.. 58 


61 


62 


59.60 


17.09 


.59.. 52 


17.35 


59.45 


17.61 


69.37 


17.87 


62 


63 


60.56 


17.37 


60.48 


17.63 


60.41 


17.89 


60.33 


18.16 


63 


64 


61.52 


17.64 


61.44 


17.91 


61.36 


18.18 


61.28 


18.44 


64 


65 


62.48 


17.92 


62.40 


18.19 


62.32 


18.46 


62.24 


18.73 


65 


66 


63.44 


18.19' 


63.. 36 


18.47 


63.28 


18.74 


63.20 


19.02 


66 


67 


64.40 


18.47 


64.32 


18.75 


64.24 


19.03 


64.16 


19.31 


67 


68 


65.37 


18.74 


65.28 


19.03 


65.20 


19.31 


65.11 


19.60 


68 


69 


66.33 


19.02 


66.24 


19.31 


66.16 


19.60 


66.07 


19.89 


69 


70 
71 


67.29 


19.29 


67.20 
68.16 


19.. 59 


67.12 


19.88 


67.03 


20.17 


70 
71 


68.25 


19.57 


19.87 


68.08 


20 . 1 7 


67.99 


20.46 


72 


69.21 


19.85 


69.12 


20.15 


69.03 


20.45 


68 . 95 


20.76 


72 


73 


70.17 


20.12 


70.08 


20.43 


69.99 


20.73 


69.90 


21.04 


73 


74 


71.13 


20.40 


71.04 


20.71 


70.95 


21.02 


70.86 


21.33 


74 


75 


72.09 


20.67 


72.00 


20.99 


71.91 


21.30 


71.82 


21.61 


76 


76 


73.06 


20 . i/5 


72.96 


21.27 


72.87 


21.59 


i 72.78 


21.90 


76 


77 


74.02 


21.22 


73.92 


21.55 


73.83 


21.87 


i 73.73 


22.19 


77 


78 


74.98 


21. .50 


■54.88 


21.83 


74.79 


22.15 


74.69 


22.48 


78 


79 


75.94 


21.78 


75.84 


22.11 


75.75 


22.44 


' 75 . 65 


22.77 


79 


80 
-81 


76.90 


22.05 


76.80 


22.39 


76.71 


22.72 


|76.61 


23.06 


80 
81 


77.86 


22.33 


77.76 


22.67 


77.66 


23.01 


,77.56 


28.34 


82 


78.82 


22.60 


78.72 


22.95 


78.62 


23.29 


,78.52 


23.63 


82 


83 


79.78 


22.88 


79.68 


23.23 


79 . 58 


23.. 57 


179.48 


23.92 


83 


84 


80.75 


23.15 


80.64 


23.51 


80.. 54 


23.86 


180.44 


24.21 


84 


85 


81.71 


23.43 


81.60 


23.79 


81.50 


24.14 


;81.39 


24.50 


85 


86 


82.67 


23.70 


82.56 


24.07 


82.46 


24.43 


i 82.35 


24.78 


86 


87 


83.63 


23.98 


83.52 


24.35 


83.42 


24.71 


83.31 


25.07 


87 


88 


84.59 


24.26 


84.48 


24.62 


84.38 


24.99 


184.27 


25.36 


88 


89 


85.55 


24.53 


85.44 


24.90 


85.33 


25 . 28 


i 85.22 


25.65 


89 


90 
91 


80.51 


24.81 


86.40 


25.18 


86.29 


25.56 


j86.18 

87.14 


25.94 
26.23 


90 
91 


87.47 


25.08 


87.36 


25.46 


87.25 


25.85 


92 


88.44 


25.36 


88.32 


25.74 


88.21 


26.13 


188.10 


26.51 


92 


93 


89.40 


25.63 


89.28 


26.02 


89.17 


26.41 


189.05 


26.80 


y3 


94 


90. CS 


25.91 


90.24 


26.30 


90.13 


26.70 


90.01 


27.09 


94 


93 


91.32 


26.19 


91.20 


26.. ^^8 


91.09 


26.98 


90.97 


27.38 


95 


96 


92.28 


26.46 


92.16 


26.86 


92.05 


27.27 


191.93 


27.67 


96 


97 


93.24 126.74 


93.12 


27.14 


93.01 


27.55 


1 92.88 


27.95 


97 


98 


94.20 27.01 


94.08 


27.42 


93.96 


27.83 


93.84 


28.24 


98 


99 


95.16 


27.29 


95.04 


27.70 


94.92 28.12 


94.80 


28.. 53 


99 


100 

i 

.2 

Q 


96.13 


27.56 


96.00 


27.98 
Lat. 


95.88 28.40 


95.76 


28.82 


100 

~i 

c 
C 


Dep. 


Lat. 


Dep. 


Dep. 


La.. 


Dep. 


Lat. 


' 74 Deg. 


73} Deg. 


73^ Deg. 


j 7^i Deg. 



36 



TKAVKRSE TABLE. 



p 

CD 


17 Deg. 


17i Deg. 


m 


Deg. 


171 Deg. 


a 
9 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.96 


0.29 


0.95 


0.30 


0.95 


0.30 


0.95 


0.30 


2 


1.91 


0.,58 


1.91 


0.59 


1.91 


0.60 


1.90 


0,61 


2 


3 


2.87 


0.88 


2.87 


0.89 


2.86 


0.90 


2.86 


0.91 


3 


4 


3.83 


1.17 


3.82 


1.19 


3.81 


1.20 


3.81 


1.22 


4 


5 


t.78 


1.46 


4.78 


1.48 


4.77 


1..50 


4.76 


1.52 


5 


6 


5.74 


1.75 


5.73 


1.78 


5.72 


1.80 


5.71 


1.83 


6 


7 


6.69 


2.05 


6.69 


2.08 


6.68 


2.10 


6.67 


2 13 




8 


7.65 


2.34 


7.64 


2.37 


7.63 


2.41 


7.62 


2.44 


8 


9 


8.61 


2.63 


8.60 


2.67 


8.. 58 


2.71 


8.57 


2.74 


9 


10 
11 


9.55 
10.52 


2.92 


9.55 


2.97 


9.54 


3.01 


9.52 


3.05 


10 
11 


3.22 


10.51 


3.26 


10.49 


3.31 


10.48 


3.35 


12 


11.48 


3.51 


11.46 


3.56 


11.44 


3.61 


11.43 


3.66 


12 


13 


12.43 


3.80 


12.42 


3.85 


12.40 


3.91 


12.. 38 


3.96 


13 


14 


13.39 


4.09 


13.37 


4.15 


13.35 


4.21 


13.33 


4.27 


14 


15 


14.34 


4.39 


14.33 


4.45 


14.31 


4.51 


14.29 


4.57 


15 


16 


15.30 


4.68 


15.28 


4.74 




4.81 


15.24 


4.88 


16 


17 


16.26 


4.97 


16.24 


5.04 


16!21 


5.11 


16.19 


5.18 


17 


18 


17.21 


5.26 


17.19 


5.34 


17.17 


5.41 


17.14 


5.49 


18 


19 


18.17 


5..'^.6 


18.15 


6 63 


18.12 


5.71 


18.10 


5.79 


19 


20 
21 


19.13 


5.85 


19.10 


.5.93! 
15.23! 


19.07 
20.03 


C.Ol 
6.31 


19.05 


6.10 


20 
21 


"20 . 08 


6.14 


20.06 


20.00 


6.40 


22 


21.04 


fi.43 


21.01 


6 52 i 


20.98 


6.62 


20.95 


6.71 


22 


23 


21.99 


6.72 


21.97 


e,.8'4| 


21.94 


6.92 


21.91 


7.01 


23 


24 


22 . 95 


7.02 


2.;. 92 


7.12 


22.89 


7.22 


22.86 


7.32 


24 


20 


23.91 


7.31 


23.88 


7 41 


23.84 


7.. 52 


23.81 


7.62 


25 


26 


24.86 


7.60 


24.83 


7.71 


24.80 


7.82 


24.76 


7.93 


26 


27 


25.82 


7.89 


25.79 


8.01 


2rj.75 


8.12 


25.71 


8.23 


27 


28 


■Zf> . 7s 


8.19 


26.74 


8.30 


26.70 


8.42 


26.67 


8.54 


28 


29 


27.73 


8.48 


27.7') 


8.60 


27.66 


8.72 


27.62 


8.84 


29 


3(1 
31 


28 . 69 
29.65 


8.77 
9.06 


28.65 
29.61 


8.90 


28.61 
29 . 57 


9.02 


28.57 


9.15 


30 
31 


9.19 


9.32 


29.. 52 


9.45 


32 


30.60 


9.36 


30.56 


9.49 


30.. 52 


9.62 


30.48 


9.76 


32 


33 


31. .56 


9.65 


31.. 52 


9.79 


31.47 


9.92 


31.43 


10.06 


33 


34 


?2.5l 


9.94 


32.47 


10.08 


32.43 


10.22 


32.38 


10.37 


34 


35 


S3. 47 


10.23 


33.43 


10.38 


33 . 38 


10.52 


33.33 


10.67 


35 


36 


34.43 


10.53 


34.. 38 


10.68 


34.33 


10.83 


34.29 


10.98 


36 


37 


35.38 


10.82 


35.34 


10.97 


35.29 


11.13 


35 24 


11.28 


37 


38 


36.34 


11.11 


36.29 


11.27 


36.24 


11.43 


30.19 


11.58 


38 


39 


.37. :W 


11.40 


37.25 


11.57 


37.19 


11.73 


37.14 


11.89 


39 


40 
41 


,38.25 


11.09 


38.20 


11.86 
12.16 


.38.15 


12.03 


38.10 


12.19 


40 
41 


39.21 


11.99 


39.16 


39.10 


12.. 33 


39.05 


12.50 


42 


40.16 


12.28 


40.11 


12.45 


40.06 


12.63 


40.00 


12.80 


42 


43 


41.12 


12.57 


41.07 


12.75 


41.01 


12.93 


40.95 


13.11 


43 


44 


42. OS 


12.86 


42.02 


13.05 


41.96 


13.23 


41.91 


13.41 


44 


45 


43.03 


13.16 


42.98 


13.34 


42.92 


13.53 


42.86 


13.72 


45 


46 


43.99 


13.45 


43.93 


13.64 


43.87 


13.83 


43.81 


14.02 


46 


47 


44.95 


18.74 


44.89 


13.94 


44.82 


14.13 


44.76 


14.33 


47 


48 


45.90 


14.03 


45.84 


14.23 


45.78 


14.43 


45.71 


14.63 


48 


49 


46.86 


14.33 


46.80 


14.. 53 


46.73 


14.73 


46.67 


14.94 


49 


50 

i 


47.82 


14.62 


47.75 


14.83 


47.69 


15.04 


47.62 


115.24 


50 

1 

5 


Dsp. 


Lat. 


Dep. 


_ Lat. 


Dep. 


Lat. 


Dep, 


1 Lat. 


73 


Deg. 


721 Deg. 


72| 


Deg. 


724 


Deg. 



TKAVERSE TABLK. 



37 



1 

51 




17 Deg. 


17i Deg. 


IT^ D.g. 


171 De„.. 



9 


Lat. 


Dep.l 


Lat. 

48.71 


Dep. 


Lat. 
48 JH 


D.P., 
15.34 


Lat. 


Dep. 


43.77 


14.91 


15.12 


48.57 


15.. 55 


51 


52 


49.73 


15.20 


49.66 


15.42 


49.59 


15.64 


49.. 52 


16.85 


52 


53 


50.68 


15.50 


50.62 


15.72 


50 . 55 


15.94 


50.48 ; 16. 16 ■ 53 


54 


51.64 


15.79 


51.. 57 


16.01 


5 1 . 50 


16.24 


51.43 16.46 , 54 


55 52.60 


16.08 


.52.53 


16.31 


52.45 


16.54 


.52.38 i 16.77 ; ,55 


56 


53.55 


16.37 


53.48 


16.61 


.53.41 


16. 84^ 


.53.33 1 17.07 1 56 


57 


54.51 


16.67 


54.44 


16.90 


.54.36 


17.14 


54.29 17.33 1 57 


58 


.55.47 


16.96| 


55.39 


17.20 


.55.32 


17.44 


.55.24 


17.68 53 


59 


56.42 


17.25 1 


50.35 


17.. 50 


56.27 


17.74 


56.10 


17.99 59 


_6U 
61 


57.38 


17. .541 


57.30 


17.79 


57.22 


18.04 


57.14 


18.29 1 60 
18.60 1 61 


58.33 


17.33 


58.26 


18.09 


5S.18 


18.34 


58.10 


6-Z 


.59.29 


18.13 


59.21 


18.39 


59.13 


18.64 


59.05 


18.90 ! 62 


63 


60.25 


18.42! 


60.17 


18.68 


GO. OS 


18.94 


GO. 00 


19.21 


63 


64 


61.20 


18.71 


61.12 j 18.98 


61.04 


19.25 1 


60.95 


19.51 


64 


65 


62.16 


19.00; 


62.08 i 19.28 


61.99 


19.55 


61.91 


19.82 


65 


66 


63.12 


19.30' 


63.03 19.57 


62.95 


19,35 


62.86 


20.12 


66 


67 


64.07 


19.59 ' 


63.99 


19.87 


63.90 


20.15 


63.81 


20.43 


67 


68 


65.03 


19.88; 64.94 


20.1.6 


64.85 


20.45] 


64.76 


20.73 


68 


69 


65.99 


20.17; 


65.90 


20.46 


65.81 : 20.75 


65.72 


21.04 


69 


70 
71 


6B.94 


20.47 I 


66.85 


20.75 


66.76 , 21.05 


66.67 


21.34 
21.65 


70 
71 


'67.90 


20.76 


67.81 


21.05 


^07. 71 


21.35 


67.62 


72 


68.85 


21.05 


68.76 


21.35 


68.67 


21.65 


68.57 


21.95 


72 


73 


09.81 


21.34, 


69.72 


21.65 


69.62 


21.95 


69.52 


22.26 


73 


74 


70.77 


21.64 


70.67 


21.94 


70.58 


22.25 


70.48 


22., 56 


74 


75 


71.72 


21.93 


71.63 


22 . 24 


71.53 


22.. 55 


71.43 


22.86 


75 


76 


72.68 


22.22 


72.58 


22.. 54 


72.48 


22.85 


72.38 


23.17 


76 


77 


73.64 


22.51 


73.. 54 


22.83 


73.44 


23.15 


73.33 


23.47 


77 


78 


74.59 


22.80 


74.49 


23.13 


74.39 


23.46 


74.29 


23.78 


78 


79 


75.-55 


23.10 


75.45 


23.43 


75.34 1 23.76 


75.24 


24.03 79 


80 


76.50 


23.39 


76.40 


23.72 


76.30 24.06 


76.19 


24.39 ' 80 


TI 


77746- 


23.68 


77.30 


24.02 


77.25 24.36 


77,14! 24.69 


81 


82 


78.42 


23.97 


78.31 


24.32 


78.20 24.66 


78.10 


25.00 


82 


83 


79.37 


24.27 


79.27 


24.61 


79.16 25.96 


79.05 


25.30 


83 


84 


80.33 


24.56 


80.22 


24.91 


80.11 25.26 


80.00 


25.61 


84 


85 


81.29 


24.85 


81.18 


25.21 


81.07 25.56 


80.95 


25.91 


85 


86 


82.24 


25.14 


82.13 


25.50 


82.02 1 25.86 


81.91 


26.22 


86 


87 


83.20 


25.44 


83.09 


25.80 


82.97 , 26.16 


82.86 


26 . 52 1 87 1 


88 


84.15 


25.73 


84.04 


26.10 


83.93 26.46 


83.81 


26.83 


88 


89 


85.11 


26.02 


85.00 


26.39 


84.88 26.76 


84,76 


27.13 


89 


90 
91 


86.07 


26.31 


85.95 


26.69 


'85.83 27.06 


85.72 


27.44 
■27.74 


90 
91 


87.02 


26.61 


86.91 


26.99 


; 86.79 27.36 


86.67 


92 


87.98 


26.90 


87.86 


27.28 


'87.:'4' 27.66 


87.62 


28.05 


92 


93 


88.94 


27.19 


88.82 


27.58 


88.70 27.97 


88.57 i 23.35 | 93 


94 


89.89 


27.48 


89.77 127.87 


89.65 28.27 


89.53 ' 28.66 94 


95 


90.85 


27.78 


90.73 


28.17 


90.60 28. .57 


90.48 128.96 95 


96 


91.81 


28.07 


91.68 


28.47 


91.56 28.87 


91.43 129.27 96 


97 


92.76 


28.36 


92.64 


28.76 


92.51 29.17 


92.38 129.57 97 


98 


93.72 


28.65 


93.59 


29.06 


93.40 29.47 


93.33:29.88 1 98 


99 


94.67 


23.94 


94.55 


29.36 


94.42 29.77 


94,29 30,18 


99 


100 

s 


95.63 


29.24 


.95.50 


29.65 


95.37 1 30,07 


95,24 1 30,49 


100 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 Lat. 


jDep. 


1 Lat, 


1 


73 Deg. 


m Deg. 


72i Deg. 


72iDeg, 



38 



TRAVERSE TABLE. 



5 
1 


18 Deg. 


18i Deg. 


18| Deg. 


181 Deg. 


f 

r 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 
0.95 


Dep. 
0.32 




0.95 


0.31 


0.95 


0.31 


1 0.95 


0.32 


2 


1.90 


0.62 


1.90 


0.63 


1.90 


0.63 


1.89 


0.64 


2 


3 


2.85 


0.93 


2.85 


0.94 


2 84 


0.95 


2.84 


0.96 


3 


4 


3.80 


1.24 


3.80 


1.25 


3 79 


1.27 


3.79 


1.29 


4 


5 


4.76 


1.55 


4.75 


1.57 


4.74 


1.59 


4.73 


1.61 


5 


6 


5.71 


1.85 


6.70 


1.88 


5.69 


1.90 


5.68 


1.93 


6 


7 


6.66 


2.16 


6.65 


2.19 


6.64 


2.22 


6.63 


2.25 


7 


Si 7.61 


2.47 


7.60 


2.51 


7.. 59 


2.54 


7.58 


2.57 


8 


9 8.56 


2.78 


8.55 


2.82 


8.. 53 


2.86 


8.52 


2.89 


9 


10 1 9.51 

11 1 10.46 


3.09 
3.40 


9.50 
10.45 


3.13 
3.44 


9.48 
10.43 


3.17 
3.49" 


9.47 
10.42 


3.21 


10 


3. ,54 ! li 


12 11.41 


3.71 


11.40 


3.76 


11.38 


? 81 


11.36 


3.86 i 12 


1.3 12.36 


4.02 


12.35 


4.07 


12.33 


4 12 


12.31 


4.18 13 


14 13.31 


4.33 


13.30 


4.38 


13.28 


4.44 


13.26 


4. .50 [ 14 


15 14.27 


4.64 


14.25 i 4.70 


14.22 


4.76 


14.20 


4.82 


15 


16 15.22 


4.94 


15.20 5.01 


15.17 


5.08 


15.15 


5.14 


10 


17 16.17 


5.25 


16.14 


5.32 


16.12 


5.39 


16.10 


5.46 


17 


18 17.12 


5.56 


17.09 


5.64 


17.07 


5.71 


17.04 


5.79 


18 


19 18.07 


5.87 


18.04 


5.95 


18.02 


6.03 


17.99 


6.11 


19 


20 


19.02 


6.18 


18.99 
19.94 


6.26 


18.97 


6.35 


18.94 
19.89 


6.43 1 20 1 


'21 


19:97 


6.49 


6.58 


19.91 


6.66 


~6.75 


21 


22 120.92 


6.80 


20.89 


6.89 


20.86 


6.98 


20.83 7.07 


22 


23 121.87 


7.11 


21.84 


7.20 


21.81 


7.30 


21.78 


7.39 


23 


24 '22.83 


7.42 


22.79 


7.52 


22.76 


7.62 


22 . 73 


7 71 


24 


25 


23.78 


7.73 


23 . 74 


7.83 


23.71 


7.93 1:23.67 


8.04' 25 


26 


24.73 


8.03 


24.69 


8.14 


24.66 


8.25 


24.62 


8.36 26 


27 


25 . 68 


8.34 


25 . 64 


8.40 


25.60 


8.57 


25.57 


8.68 27 


28 


26.63 


8.65 


26.59 


8.77 


26.55 


8.88 


26.51 


9.00 1 28 i 


29 127.. 58 


8.96! 


27.54 


9.08 


27.50 


9.20 


27.46 


9.32 


29 


30 128.53 


9.27i 


28.49 
29.44 


9.39 


28.45 


9.52 
9.84 


28.41 
29.35 


9.64 


3C 
31 


31 


29.48 


9.58 


9.71 


29.40 


9.96 


32 


30.43 


9.89 


30.39 


10.02 


30.35 


10.15 


30.30 


10.29 1 32 1 


33 


31.38 


10.20 


31.34 


10.33 


31.29 


10.47 


31.25 


10.61 33 ! 


34 


.32.34 


10.51 


32.29 


10.65 1 


32 . 24 


10.79 


32.20 


10.93 


34 


35 


33.29 


10.82 


33.24 


10.96 1 


33.19 


11.11 


.33.14 


11.25 


35 


36 


34.24 


11.12 


34.19 


11.271 


34,14 


11.42 


34.09 


11.57 


36 


37 


35.19 


11.43 


35.14 


11.59 


35.09 


11.74 


35.04 


11.89 


37 


38 


36.14 


11.74 


36.09 


11.90 


36.04 


12.06 


35.98 


12.21 


38 


39 


37.09 


12.05 


37.04 


12.21 


36.98 


12.37 


36.93 


12.54 


39 


40 38.04 


12.36 


37.99 


12.53 


37.93 


12.69 


37.88 
'38.82 


12.86 40 1 


41 


38.99 


12.67 


38 . 94 


12.84 


38.88 


13.01 


13.18 


41 


42 


39 . 94 


12.98 


39.89 


13.15 


39.83 


13.33 


39.77 


13.. 50 


42 


43 


40.90 


13.29 


40.84 


13.47 


40.78 


13.64 


40.72 


13.82 


43 


44 41.85 


13.60 


41.79 


13.78 


41.73 


13.96 


41.66 


14.14 


44 


45 142.80 


13.91 


42.74 


14.09 


42.67 


14.28 


42.61 


14.40 


45 


46 43.75 


14.21 


43.69 


14.41 


43.62 


14.60 


43.56 


14.79 


46 


47 144.70 


14.52 


44.64 


14.72 


44.57 


14.91 


44.51 


15.11 


47 


48 45.65 


14.83 


45.59 


15.03 


45.52 


15.23 


45.45 


15.43 


48 


49 46.60 


15.14 


46.54 


15.35 


46.47 


15.55 


46.40 


15.75 


49 


50 47.55 1 15.45 1 


47.48 


JJ>.66_ 


47.42 


15.87 


47.35 


16.07 


50 


i 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


c 

5 


l| 


72 Deg. 


711 Deg. 


7HI 


)eg. 


7U Deg. 



TRAVKRSE TABLF. 



2 

i 

51 


18 Deg. 


18i Deg. 


18^ Deg. 


1 181 Deg. 




Lat. 


Dep. 


Lat. Dep. 


Lat. 


j Dep. 
,"l6Tl8" 


j-La,. 
48 .29 


Dep. 
16.39 


18.50 


15.76 


48.43 i 15.97 


Us.. 36 


52 


49.45 


16.07 49.38 


16.28 


49.31 1 16.50 


! 49.24 


16.71 


62 


53 


50.41 


16.38 1 50.33 


16.60 


50.26 ' 16.82 


50.19 


17.04 


53 


54 


51.36 


16.69 ]51.28 


16.91 


,51.21 1 17.13 


51.13 


17.36 


54 


55 '52.31 


17.00 52.23 


17.22 


.52.16 1 17.45 


52.08 


17.68 


55 


66 


53.26 


17.30 


53.18 


17. .54 


153. 11 17.77 


53.03 


18.00 56 


57 


54.21 


17.61 


54.13 


17.85 


54.05 18.09 i 53.98 


18.32 57 


58 


55.16 


17.92 


55.08 


18.16 


65.00 18.40 1 54.92 


18.64 j 58 


59 


.56.1] 


18.23 


.56.03 


18.48 


55.95 i 18.72 | 55.87 


18.96 1 59 


GO 
61 


57.06 


18.54 


56.98 


18.79 


56.90 ' 19.04 


56.82 


19.29 


_60 


58.01 


18 85 


57.93 I 19. 10 


57.85 19.36 


57.76 


19. 6f 


61 


62 


.58.97 


19.16 


.58.88 1 19.42 


58.80 19.67 


58.71 


19.93' 62 


63 


59.92 


19.47 


59.83 19.73 


59.74 , 19.99 


59.66 


20 . 25 : 63 


61 


60.87 


19.78 


60 . 7S 1 20 . 04 


60.69 20.31 


60.60 


20 . 57 i 64 


65 


61.82 


20.09 


61.73 20.36 


61.64 20.62 


61.55 


20.89 : 05 


66 


62.77 


20.40 


62.68 1 20.67 


62.59 I 20.94 


62.50 


21.22 ; 66 


67 


63.72 


20.70 


63.63 20.98 


63.54 121.26 


63.44 


21.54 ! 67 


68 


64.67 


21.01 


64.58 21.30 


64.49 


21.58 


64.39 


21.86 1 68 


69 


65.62 


21.32 


65.53 ! 21.61 


65.43 


21.89 


65 . 34 


22.18 ; 69 


70 
71 


66.57 


21.63 


66.48 


21.92 


66.38 


22.21 


66.29 


22.50 1 70 

22.82 ! 71 


67.53 


21.94 


67.43 


22.23 


67.33 


22.53 


67.23 


72 


68.48 


22.25 


68.38 


22.55 


68.28 


22.85 ! 68.18 


23.14 72 


73 


69.43 


22.56 


69.. 33 


22.86 


69.23 


23.16 1 69.13 23.47 1 73 | 


74 


70.38 


22.87 


70.28 


23.17 


70.18 


23.48 1; 70.07 


23.79 t 74 1 


75 


71.33 


23.18 


71.23 


23.49 


71.12 


23.80 : 71.02 


24.11 


75 


76 


72.28 


23.49 


72.18 


23 . 80 


72.07 


24.12 i 71.97 


24.43 


76 


77 


73.23 


23.79 


73.13 


24.11 


73.02 


24.43 


72.91 


24.75 


77 


78 


74.18 


24.10 


74.08 


24.43 


73.97 


24.75 


73.86 


25.07 


78 


79 


75.13 


24.41 


75.03 


24.74 


74.92 


25.07 


74.81 


25.39 


79 


80 
81 


76.08 
77.04 


24.72 


75 . 98 


25.05 


75.87 


25.38 


75.75 
76.70 


25.72 1 80 
26.04 i 81 


25.03 


76.93 


25.37 


76.81 


25.70 


82 


77.99 


25.34 


77.88 


25.68 


77.76 


26.02 


77.65 


26.. 36' 82 


83 


78.94 


25.65 


78.83 


25.99 


78.71 


26.34 


78.60 


26.68 83 


84 


79.89 


25.96 


79.77 


26.31 


79.66 


26.65 


79.54 


27.00 1 84 


85 


80.84 


26.27 


80.72 


26.62 


80.61 


26.97 


80.49 


27.32 85 


86 


81.79 


26.58 


81.67 


26.93 


81.56 


27.29 


81.44 


27.64 86 


87 


82.74 


26.88 


82.62 


27.25 


82.50 


27.61 


82.38 


27.97 87 


88 


83.69 


27.19 


83.57 i 27.56! 


83.45 


27.92 


83.33 


28. 2Q 88 


89 


84.64 


27.50 


84.52 ' 27.87 i 


84.40 


28.24 


84.28 


28.61 89 


90 
91 


85.60 
86.55 


27.81 
28.12 


85.47 128.18! 


85.35 


28.56 


85.22 


28.93 90 
29.25; 91 


86.42 I 28.50 ! 


86.30 


28.37 


86.17 


92 


87.50 


28.43 


87.37 1 28.81 


87.25 129.19 


Si'. 12 


29.57 j 92 


93 


88.45 


28 . 74 


88.32 1 29.12 


88.19 29.51 


88.06 


29.89 93 


94 


89.40 


29.05 


89.27 ! 29.44 ! 


89.14 \ 29.83 


89.01 


30.22 1 94 


95 


90.35 


29.36 


90.22 


29 . 75 1 


90.09 1 30.14 


89.96 


30.54 ; 95 


96 


91.30 


29.67 


91.17 


30.06 1 


91.04 


30.46 


170.91 


30.86 96 


97 


92.25 


29.97 


92.12 


30.38: 


91.99 


30.78 


91.85 


31.18 97 


98 


93.20 


30.28 


93.07 30.69' 


92.94 


31.10 


92.80 


31.50 98 


99 


94.15 


30.59 


94.02 31.00; 


93.88 


31.41 


93.75 


31.82. 99 


100 

1 


95.11 


30.90 


94.97 
Dep. 


31.32 :| 94.83 


31.73 


94.69 


32.14 100 


Dep. 


Lat. 


Lat. ! 


Dep. 


Lat. 


Dep. 


Lat 


8 


72 1 


)eg. 


71} Deg. \ 


71iDeg. 


7U Deg. 


1 
b 



40 



TRAVFRSE TABLE. 



B 


19 Deg. 


19i Deg. 


19i 


Deg. 


191 Deg. 


B 


Lat. 
0.95 


Dep. 

"oTsF 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep, 


0.94 


0.33 


0.94 


0..33 


0.94 


0.34 


I 


2 


1.89 


0,65 


1.89 


0,66 


1.89 


0.67 


1.88 


0.68 


2 


3 


2.84 


0.98 


2.83 


0,99 


2.83 


l.UO 


2 82 


1.01 


3 


4 


3.78 


1.30 


3.78 


1..32 


3.77 


1.34 


3.76 


1,35 


4 


5 


4.73 


1.63 


4.72 


1,65 


4.71 


1.67 


4.71 


1,69 


5 


6 


5.67 


1.95 


5,66 


1,98 


5.66 


2.00 


5.65 


2,03 


fi 


7 


6.62 


2.28 


6,01 


2,31 


6.60 


2.34 


6.59 


2,37 


7 


8 


7.56 


2.60 


7,55 


2,64 


7.54 


2.67 


7.53 


2,70 


8 


9 


8.51 


2.93 


8.50 


2.97 


8.48 


3.00 


8.47 


3,04 


9 


10 


9.46 


3.26 


9.44 
10.38 


3.30 


9.43 


3.34 


9.41 


3,38 


10 


11 


10,40 


3,58 


3.63 


10.37 


3.67 


10.35 


3,72 


11 


12 


11.35 


3.91 


11. .33 


3,96 


11.31 


4.01 


11.29 


4,06 


12 


13 


12.29 


4.23 


12.27 


4.29 


12.25 


4,34 


12.24 


4.39 


13 


14 


13.24 


4., 56 


13.22 


4.62 


13.20 


4.67 


13,18 


4.73 


14 


15 


14.18 


4.88 


14,16 


4.95 


14,14 


5,01 


14,12 


5.07 


15 


16 


15.13 


5.21 


15,11 


5.28 


15,08 


5,34 


15,06 


5,41 


16 


17 


16.07 


5.-53 


16,05 


5.00 


16,02 


5,67 


16,00 


5,74 


17 


18 


17.02 


5.86 


16.99 


5.93 


16,97 


6,01 


16,94 


6,08 


18 


19 


17.96 


6.19 


17.94 


6.26 


17,91 


6.34 


17.88 


6.42 


19 


20 
21 


18.91 


6.51 


18.88 


6.59 


18,85 


6.68 


18,82 


6.76 


20 
21 


19.56 


0.84 


19.83 


6.92 


19.80" 


7,01 


19,76 


7.10 


22 


20,80 


7.16 


20.77 


7.25 


20.74 


7.34 


20.71 


7.43 


22 


23 


21,75 


7.49 


21.71 


7.. 58 


21.68 


7.68 i' 21.65 


7.77 


23 


24 


22.69 


7.81 


22 . 66 


7.91 


22,62 


8.01 22.-59 


8.11 


24 


25 


23.64 


8.14 


23,60 


8,24 


23,57 


8.35 


23.53 


8.45 


25 


26 


24.-58 


8.46 


24,55 


8,-57 


24.51 


8.68 


24.47 


8.79 


26 


27 


25.. 53 


8.79 


25,49 


8,90 


25.45 


9.01 


25.41 


9.12 


27 


28 


26,47 


9.12 


26,43 


9,23 


26.39 


9.35 


26.35 


9.46 


28 


29 


27.42 


9,44 


27.38 


9,-56 


27.34 


9.68 


27.29 


9.80 


29 


30 


28.37 


9,77 


28,32 


9,89 


28.28 


10.01 


28.24 


10.14 


30 


31 


29.31 


10,09 


29,27 


10,22 


29.22 


10,35 


29.18 


10.48 


3i 


32 


30.26 


10,42 


30,21 


10,55 


30,16 


10,68 


30.12 


10.81 


32 


33 


31.20 


10.74 


31,15 


10,88 


31,11 


11,02 


31.06 


11.15 


33 


34 


32.15 


11.07 


32,10 


11,21 


.32,05 


11,35 


32.00 


11.49 


34 


35 


33.09 


11,39 


33,04 


1 1 , 54 


32.99 


11,68 


32.94 


11.83 


35 


36 


34.04 


1 1 , 72 


33,99 


11.87 


33.94 


12,02 


33.88 


12.17 


36 


37 


34.98 


12,05 


34,93 


12.20 


34.88 


12,35 


34.82 


12.50 


37 


38 


35.93 


12,37 


35.88 


12.-53 


35.82 


12,68 


35.76 


12.84 


38 


39 


36.88 


12,70 


36.82 


12.86 


36.70 


13.02 


.36.71 


13.18 


39 


40 


37.82 


13,02 


37.76 
38.71 


13.19 


37.71 


13.35 
13.69 


37.65 


13.-52 


40 
41 


4f 


38.77 


13,35 


13.-52 


38.05 


38.59 


13.85 


42 


39.71 


13,*7 


39,65 


13.85 


39.59 


14.02 


39.53 


14.19 


42 


43 


40.66 


14.00 


40.60 


14.18 


40,-53 


14.35 


40,47 


14.. 53 


43 


44 


41.60 


14.32 


41.. 54 


14.51 


41,48 


14.69 


41,41 


14.87 


44 


45 


42.55 


14,65 


42.48 


14.84 


42,42 


15.02 


42,35 


15.21 


45 


46 


43.49 


14,98 


43.43 


15.17 


43,36 


15.36 


43,29 


15.-54 


46 


47 ! 44,44 


15,30 


44.37 


15.-50 


44.-30 


15.69 


44,24 


15.88 


47 


48 145.38 


15,63 


45.32 


15.83 


45,25 


16.02 


45.18 


16.22 


48 


49 


46.33 


15.95 


46.26 


16,15 


46.19 


16.36 


46.12 


16.56 


49 


50 


47.28 


16.28 


47.20 


16,48 


47.13 


16^,^ 


47.06 


16.90 


50 


c 
1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep, 


Lai. 


1 


71 1 


)eg. 


■ 

70.1 


Deg. 


70il 


Deg. 


70i 


Deg. 



TRAVERSE TABLE. 



41 



a 

i 

51 


19 Deg. 


191 Deg. 


19^ Dog. 


19| Deg. 




K 
P 

'51 


Lat. 1 Dep. 


Lat. 


Dep. 


Lat. 


Dop. 


Lat. 


Dep. 


48.22 16.60 


48.15 


T6."8r 


48.07 


17.02 


48.00 


17.23 


52 


49.17 16.93 


49.09 


17.14 


49.02 


17.36 


48,94 


17.57 


52 


53 


.50.11 17.26 


50.04 


17.47 


49.96 


17.69 


49.88 


17.91 


53 


54 


51.06 17.58 


.'SO. 98 


17.80 


.50.90 


18.03 1 


.50.82 


18.25 


54 


55 


52.00 1 17.91 j 


51.92 


18.13 


51.85 


18.36 


51.76 


18.-59 


.55 


56 


52.95 18.23! 


52.87 


18.46 


.52.79 


18.69 


52.71 


18.92 




57 


53.89 


18.. 56, 


53.81 


18.79 


53.73 


19.03 


-53.65 


19.26 


57 


58 


.54.84 


18.88 


54.76 19.12 1 


.54.67 


19.36 


-54.-59 


19.60 


58 


59 


55.79 


19.21 


55 . 70 


19.45! 


.55.62 


19.69 


55 . 53 


19.94 


59 


60 
61 


50.73 19.. 53 


56 . 65 


19.78 


56.56 
57 . 50 


20.03 
20.36 


.56.47 


20 . 27 


60 
61 


57 . 68 


19.86 


57.59 


20.11 


-57.41 


20.61 


62 


58.62 


20.19 


.58.-53 


20.44 


58.44 


20.70 


58.35 


20 95 


62 


63 


59.-57 


20.51 


59.48 


20.77 


59.39 


21.03 


59 . 29 


21.29 


63 


64 


60.51 


20.84 


60.42 


21.10 


60.33 


21.36 


60.24 


21.63 


64 


65 


61.46 


21.16 


61.37 


21.43 


01.27 


21.70 


61.18 


21.96 


65 


66 


62.40 


21.49 


62.31 


21.76 


62.21 


22.03 


62.12 


22.30 


66 


67 


63.35 


21.81 


63.25 


22 . 09 


63. iO 


22.37 


63.06 


22 . 64 


67 


68 


64.30 


22.14 


64.20 


22.42 


64.10 


22 . 70 


64.00 


22.93 


68 


69 


65.04 


22.40 


65.14 


22.75 


65.04 


23.03 


64.94 


23.32 


69 


<0 
71 


66.19 


22.79 


66.09 


23 . 08 


65.93 


23.37 


65.88 
66.82 


23 . 65 


70 

71 


67.13 


23.12 


07.03 


23.41 


66 . 93 


23.70 


23.99 


72 


08.08 


23.44 


67.97 


23.71 


67.87 


24.03 


67.76 


24.33 


72 


73 


69.02 


23.77 


68 . 92 


24.07 


03.81 


24.37 


68.71 


24 . 67 


73 


74 


69.97 


24.09 


69.86 


24.40 


09.76 


24.70 


69.65 


25.01 


74 


75 


70.91 


24.42 


70.81 


24 . 73 


70.70 


2'.. 04 


70.. 59 


25.34 


75 


76 


71.86 


24.74 


71.75 


25.06 


71.64 


25.37 


1 71. .53 


25.63 


76 


77 


72.80 


25.07 


72.69 


25.39 


72.-58 


25 . 70 


72.47 


26.02 


77 


78 


73.75 i 25.39 


73.84 


25.72 


73.. 53 


26.04 


73.41 


26.36 


78 


79 


74.70; 25.73 


74.-58 


26.05 


74.47 


26.37 


74.35 


26 . 70 


79 


80 
81 


75.64 


26.05 


75.-53 


26.38 


75.41 


26 . 70 


75.29 


27.03 


80 
81 


76.59 


26.37 


76.47 


26 . 70 


76.35 


27.04 


76 .24 


27.37 


82 


77.53 


26.70 


77.42 


27.03 


77.30 


27.37 


77.18 


27 . 7 1 


82 


83 


78.48 


27.02 


78.36 


27.36 


78.24 


27.71 


78.12 


23.05 


83 


84 


79.42 


27.35 


79.30 


27.69 


79.18 


23.04 


79.06 


23 . 39 


84 


85 


80.37 


27.67 


80.25 


28.02 


80.12 


23.37 


80.00 


23 . 72 


85 


86 


81.31 


28.00 


81.19 


28.35 


81.07 


23.71 


80.94 


29.06 


86 


87 


82.26 


28.32 


82.14 


28 . 63 


82.01 


29.04 


1 81.88 


29.40 


87 


88 


vS3.21 


28.65 


83.08 


29.01 


92.95 


29.37 


1 82.82 


29 . 74 


88 


89 


84.15 


28.98 


84.02 


29 . 34 


83 . 90 


29.71 


, 83.76 


30.07 


89 


90 
91 


85.10| 29.30 


84.97 


29.67 


84.84 


30.04 


84.71 


30.41 


90 
91 


86.04! 29.63 


85.91 


30.00 


85.78 


30.38 


85.65 


30.75 


92 


86.99 29.95 


86.86 


30 . 33 


86.72 


30.71 


86.-59 


31.09 


92 


93 


87.93,30.28 


87.80 


30.66 


87.67 


31-04 


37.. 53 


31.43 


93 


94 


88.88 1 30.60 


88.74 


30.99 


188.6I 


31.38 


88.47 


31.76 


94 


95 


89.82 


30.93 


89.69 


31.32 


189.-55 


31.71 


1 89-41 


32.10 


95 


96 


90.77 


31.25 


90.63 


31.65 


90.49 


.32.05 


90.35 


32.44 


96 


97 


91.72 


31.58 


91. .58 


31.98 


91.44 


32.38 


91.29 1.32.78 


97 


98 


92.66 


31.91 


92.-52 


32.31 


92.38 


32.71 


92.24 


33 . 1 2 


98 


99 


93.61 


33.23 


93.46 


32.6'! 


93.32 i 33.05 


93.18 


.33.45 


99 


100 

T 

Q 


94.55 


32.56 


94.41 


32.97 


94.26 


33., 38 
Lat. 


94.12 
Dep. 


33^ 
Lat. 


J 

1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


71 Deg. 


701 Deg. 


70i Deg. 


70i Deg. 



42 



TRAVERSE TABLE. 





20 


Deg. 


m Deg. 


201 


Deg. 


201 


Deg. 


i 

1 


Lat. 
0.94 


1 Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 

" 0.35 


0.34 


0.94 


0..35 


0.94 


0.35 


0.94 


2 


1.88 


0.68 


1.88 


0.69 


1.87 


0.70 


1.87 


0.71 




3 


2.82 


1.03 


2.81 


1.04 


2.81 


1.05 


2.81 


1.06 


3 


4 


3.76 


1.37 


3.75 


1.38 


3.75 


1.40 


3.74 


1.42 


4 


5 


4,70 


1.71 


4.69 


1.73 


4.68 


1.75 


4.68 


1.77 


5 


6 


5.64 


2.05 


5.63 


2.08 


5.62 


2.10 


5.61 


2.13 


6 


7 


6.58 


2.39 


6.67 


2.42 


6.56 


2.45 


6.55 


2.48 


7 


8 


7.52 


2.74 


7.51 


2.77 


7.49 


2.80 


7.48 


2.83 


8 


9 


8.46 


3.08 


8.44 


3.12 


8.43 


3.15 


8.42 


3.19 


9 


10 

11 


9.40 


3.42 


9.38 
10.32 


3.46 


9.37 


3.50 


9.35 


3.. 54 


10 
11 


10.34 


3.76 


3.81 


10.30 


3.85 


10.29 


3.90 


12 


11.28 


4.10 


11.26 


4.15 


11.24 


4.20 


11.22 


4.25 


12 


13 


12.22 


4.45 


12.20 


4.50 


12.18 


4.55 


12.10 


4.61 


13 


14 


13.16 


4.79 


13.13 


4.85 


13.11 


4.90 


13.09 


4.96 


14 


15 


14.10 


5.13 


14.07 


5.19 


14.05 


5.25 


14.03 


5.31 


15 


16 


15.04 


5.47 


15.01 


5.. 54 


14.99 


5.60 


14.96 


6.67 


16 


17 


15.97 


5.81 


15.95 


5.88 


15.92 


5.95 


15.90 


6.02 


17 


18 


16.91 


6.16 


16.89 


6.23 


16.86 


6.30 


16.83 


6.38 


18 


19 


17.85 


6.50 


17.83 


6.. 58 


17.80 


6.65 


17.77 


6.73 


19 


20 


18.79 


6.84 


18.76 


6.92 


18.73 


7.00 


•18.70 


7.09 


20 


21 


19.73 


7.18 


19.70 


7.27 


19.67 


7.35 


19.64 


7.44 


21 


22 


20.67 


7.52 


20.64 


7.61 


20.61 


7.70 


20.. 57 


7.79 


22 


23 


21. G] 


7.87 


21.58 


7.96 


21. .54 


8.05 


21.51 


8.15 


23 


24 


22.55 


8.21 


22 . 52 


8.31 


22.48 


8.40 


22.44 


8 . 50 


24 


25 


23.49 


8.55 


23.45 


8.65 


23.42 


8.76 


23.38 


8.86 


25 


26 


24.43 


8.89 


24.39 


9.00 


24.35 


9.11 


24.31 


9.21 


26 


27 


25.37 


9.23 


25.33 


9.35 


25.29 


9.46 


25.25 


9.57 


27 


28 


26.31 


9.58 


26.27 


9.69 


26.23 


9.81 


26.18 


9.92 


28 


29 


27.25 


9.92 


27.21 


10.04 


27.16 


10.16 


27.12 


10.27 


29 


30 


28.19 1 10.26 


28.15 


10.38 


28.10 


10.51 


28.05 


10.63 


30 


31 


29.13 


10.60 


29.08 


10.73 


29.04 


10.86 


28.99 


10.98 


31 


32 


30 . 07 


10.94 


30.02 


11.08 


29 . 97 


11.21 


29.92 


11.34 


32 


33 


31.01 


11.29 


30.96 


11.42 


30.91 


11.56 


30.86 


11.69 


33 


34 


31.95 


11.63 


31.90 


11.77 


31.85 


11.91 


31.79 


12.05 


34 


35 


.32.89 


11.97 


32.84 


12.11 


32 . 78 


12.26 


32.73 


12.40 


35 


38 


33.83 


12.31 


.33 . 77 


12.46 


33.72 


12.61 


33.66 


12.75 


36 


37 


.34.77 


12.65 


34.71 


12.81 


34.66 


12.96 


34.60 


13.11 


37 


38 


35.71 


13.00 


35.65 


13.15 


35 . 59 


13.31 


35 , 54 


13.46 


38 


39 


36.05 


13.34 


30 . 59 


13.50 


36.. 53 


13.66 


.36.47 


13.82 


39 


40 


37.59 


13.68 


37. .53 


13.84 


37.47 


14.01 


37.41 


14.17 


40 


"^41 


38 . 53 


14.02 


38.47 


14.19 


38.40 


14.36 


38.34 


14.53 


41 


42 


39.47 


14.36 


39.40 


14.. 54 


39.34 


14.71 


39.28 


14.88 


42 


43 


40.41 


14.71 


40.34 


14.88 


40.28 


15.06 


40.21 


15.23 


43 


44 


41.35 


15.05 


41.28 


15.23 


41.21 


15.41 


41.15 


15.59 


44 


45 


42.29 


15.39 


42 . 22 


15. .58 


42.15 


15.76 


42.08 


15.94 


45 


46 


43.23 


15.73 


43.16 


15.92 


43.09 


16.11 


43.02 


16. .30 


46 


47 


44.17 


16.07 


44.09 


16.27 


44.02 


16.46 


43.95 


16.65 


47 


48 


45.11 


16.42 


45.03 


16.61 


44.96 


16.81 


44.89 


17.01 


48 


49 


46.04 


16.76 


45.97 


16.96 


45.90 


17.16 


45.82 


17.36 


49 


50 

Q 


46.98 


17.10 


46.91 


17.31 


46.83 


17.51 


46.76 


17.71 


50 

c 

£ 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


70 Deg. 


691 


Deg. 


en 


Deg. 


69i 


Dog 



TUAVEKSK TAliLK. 



43 



'51 


20 Deg. 


20i Dog, 


201 Deg. 


201 Deg. 


2 
"51 


Lat. Dep. 


Lat, 


Dep. 

T7,65 


Lat. 1 Dep. 


Lat, 

4776T 


Dep. 


47.92; 17,44 | 


47 35 


47.771 17.86 


18.07 


52 


48.86 1 17.79 j 


48.79 


18.00 


43,71 18.21 i 


48,63 


18.42 


52 


53 


49.801 18.13 


49.72 


IS. 34 


49.64; 18.56 1 


49.56 


18,78 


53 


54 


50.74 18.47 


50.66 


18.69 t 


.50.58 1 18.91 1 


.50.50 


19.13 


54 


53 


51. 6S 18.81 j 


51.60 


19.04 


51.. 52 


19,26 1 


51.43 


19.49 


55 


5G 


,52.62 19.15 


.52.54 


19.38 


.52.45 


19.61 1 


52.37 


19.84 


66 


57 


,53.56 i 19.. 50 


53,48 


19.73 


53.39 


19.96 1 


.53,30 


20.19 


57 


5S 


.54.50 19.84 


54.42 


20.07 


54.33 


20.31 ; 


54.24 


20.55 


58 


59 


55.44 j 20.18 


5 5.. 35 


20.42 


55 . 26 


20.66 1 


55.17 


20 . 90 


59 


60 
fil 


5n.3S : 20.. 52 
7>7T:V2 ' 20.86 


56.29 


20.77 


56.20 
.57.14 


21.01 
21.36 


56,11 


21.20 
21.61 


60 
61 


57.23 


21.11 


57,04" 


6-2 


5.S.23 21.21 


.58.17 


21.46 


.58.07 


21,71 


57,98 


21.97 


62 


0:5 


59.20, 21.. 55 


59.11 


21.81 


59.01 


22,06 


58,91 


22 . 32 


63 


r,i 


60.14 1 21.89 


60,04 : 22,15 1 


59.95 


22.41 


59,85 


22.67 


64 


r,.-, 


6 1 . OS ^ 22 . 23 


60.98 j 22.50 


60.88 


22.76 


60.78 


23.03 


65 


Ofi 


62.02' 22.57 


61.92 


22.84 


61.82 


23.11 


61,72 


23.38 


66 


67 


62.98 22.92 


62.86 


23.19 


62.76 


23.46 1 


62.65 


23.74 


67 


G8 


63.90 123.26 


63,80 


23,54 


63.69 


23.81 


63.59 


24.09 


68 


6'J 


64.84 1 23.60 


64.74 


23.83 


64,63 


24.16 


64,52 


24.45 


69 


70 
71 


65.78 23.94 
66.72 1 24.28 


65.67 
66.61 


24.23 


65.57 


24.51 


65.46 


24.80 


70 
71 


24,5? 


66.50 


24.86 


66.39 


25.15 


72 


67.66 i 24.63 


67.55 


24.92 


67.44 


25.21 


67.33 


25,51 


72 


73 


68.60 i 24,97 


68.49 


25,27 


68.38 


25.57 


68.26 


25,86 


73 


74 


69.54 : 25.31 


69.43 


25.61 


69.31 


25.92 


69,20 


26,22 


74 


75 


70.48 25.65 


70.36 


25.96 


70.25 


26,27 


70,14 


26.57 


75 


76 


71.42 . 25.99 


71.30 


26.30 


71.19 


26,62 


71.07 


26.93 


76 


77 


72.36 ' 26.34 


72.24 


26.65 


72.12 


26.97 


72,01 


27.28 


77 


78 


73 . 30 ; 26 . 68 


73.18 


27.00 


73.06 


27.32 


72,94 


27.63 


78 


79 


74.24:27.02 


74.12 


27.34 


74.00 


27.67 


! 73,88 


27,99 


79 


80 
81 


75.18 1 27.36 
76.12 1 27.70 


75.06 


27.69 
28.04 


74,93 128,02 


74,81 
75 . 75 


28,34 


80 


75.99 


75,87 


28.37 


28,70 


81 


82 


77.05 23.05 


76.93 


28.38 


76.81 


28 . 72 


76.68 


29.05 


82 


83 


77.99 ! 28.39 


77.37 


28.73 


77.74 


29,07 


77.62 


29.41 


83 


84 


78 . 93 j 28 . 73 


78.81 


29.07 


78.63 


29.42 


78 . 55 


29.76 


84 


85 


79.87 29.07 


79.75 


29.42 


79.62 


29,77 


79.49 


30.11 


85 


86 


80.81 


29.41 


80.68 


29.77 


80,55 


30.12 


80,42 


30.47 


86 


87 


81.75 


29 . 76 


81.62 


30.11 


81,49 


30,47 


181,38 


30.32 


87 


88 


82.69 


30.10 


82 . .56 


30.46 


82,43 


30,82 


182.29 


31,18 


88 


89 


83.63 


30.44 


83.. 50 


30.80 


S3, 36 


31.17 


83,23 


31,-53 


89 


90 
91 


84.57 


30.73 


84.441 31,15 


84,30 


31,52 


84,16 


31,89 


90 
91 


85.51 


31.12 


85.-38 


31,50 


85,24 


31,37 


135,10 


32.24 


92 


85.45 


31.47 


86.31 


31,84 


86.17 


32,22 


86.03 


32.59 


92 


93 


87.39, 31.81 


87.25 


32.19 


87.11 


.32.57 


86.97 


32.95 


93 


91 


8S.33' 32.15 


88.19 


32.. 54 


88 . 05 


32.92 


87,90 133.30 


94 


95 


89.27 32.49 


89.13 


32.88 


88.98 


33.27 


188,34 


33 . 66 


95 


95 


90.21 ; 32.83 


90.07 


33.23 


89.92 1 33.62 


89,77 


34.01 


96 


97 


91.15 133.18 


91.00 


33 . 57 


90.86 33.97 


90.71 


34.37 


97 


9S 


93.09' 33.. 52 


91.94 


,33.92 


91.79134.32 


91.64 


34.72 


98 


99 


93.03 33.86 


92.88 


34.27 


92.73 34.67 


92.. 58 


35.07 


99 


10_0 
.1 


: 93.97. 34,20 


93.82 


34,61 


93.67 1 35,02 


93.51 


35.43 


100 

c 

1 "" 


' Dep. 

i 70 


Lat. 


Dep. 


Lat. 


Dep. j Lat, 


Dep. 


Lat. 


Deg. 


..1 


Deg. 


69 i 


Deg 


69i 


Deg 



44 



TRAVKKSE TAI5LE. 





21 Deg. 


21i Deg. 


211 


Deg. 


21i Deg. 




Lat. 


Dep. 1 


Lat. 


Dep. 
"0.36 


Lat. 


Dep. 


Lat. 


Dep. 


0.93 


0.36 1 0.93 


0.93 


0.37 


0.93 


0.37 


2 


1.87 


0.72 


1.86 


0.72 


1.86 


0.73 


1.86 


0.74 


2 


3 


2.80 


1.08 


2.80 


1.09 


2.79 


1.10 


2.79 


1.11 


3 


4 


3.73 


1.43 


3.73 


1.45 


3.72 


1.47 


3.72 


1.48 


4 


6 


4.67 


1.79 


4.66 


1.81 


4.65 


1.83 


4.64 


1 .85 


5 


6 


5.60 


2.15 


5.59 


2.17 


5.58 


2.20 


5.57 


2.22 


6 


7 


6.54 


2.51 


6.52 


2.54 


6.51 


2.57 


6,50 


2.59 


7 


8 


7.47 


2.87 


7.46 


2.90 


7.44 


2.93 


7.43 


2.96 


8 


9 


8.40 


3.23 


8.39 


3.26 


8.37 


3.30 


8.36 


3.34 


9 


111 


9.34 


3.58 


9.32 


3.62 


9.30 


3.67 


9.29 


3.71 
4.08 


10 
11 


10.27 


3.94 


10.25 


3 . 99 


10.23 


4.03 


10.22 


)2 


11.20 


4.30 


11.18 


4.35 


11.17 


4.40 


11.15 


4.45 


12' 


13 


12.14 


4.66 


12.12 


4.71 


12.10 


4.76 


12.07 


4.82 


13 


14 


13.07 


5.02 


13.05 


5.07 


13.03 


5.13 


13.00 


5.19 


14 


ir, 


14.00 


5.38 


13.98 


5.44 


13.96 


5.. 50 


13.93 


5.56 


15 


ic 


14.94 


5.73 


14.91 


5.80 


14.89 


5.86 


14.86 


5.93 


16 


17 


15.87 


6.09 


15.84 


6.16 


15.82 


6.23 


15.79 


6.30 


17 


18 


16.80 


6.45 


16.78 


6.52 


16.75 


6.60 


16.72 


6.67 


18 


19 


17.74 


6.81 


17.71 


6.89 


17.68 


6.96 


17.65 


7.04 


19 


^ 


18.67 


7.17 


18.64 


7.25 


18.01 


7.33 


1 8.. 58 


7.41 


20 


21 


19.61 


7.53 i 19.57 


7.61 


19. .54 


7.70 


19.50 


7.78 


21 


22 


20.54 


7.88 


20.50 


7.97 


20.47 


8.06 


20.43 


8.15 


22 


23 


21.47 


8.24 


21.44 


8.34 


21.40 


8.43 


21.36 


8.. 52 


23 


24 ] 22.41 


8.60 


22.37 


8.70 


22.33 


8.80 


22.29 


8.89 


24 


25 


23.34 


8.96 


23.30 


9.06 


23.26 


9.16 


23.22 


9.20 


25 


26 


24.27 


9.32 


24.23 


9.42 


24.19 


9.53 


24.15 


9.63 


20 


27 


25.21 


9.68 


25.16 


9.79 


25.12 


9.90 


25.08 


10,01 


27 


28 


20.14 


10.03 


20.10 


10.15 


26.05 


10.26 


26.01 


10 38 


23 


29 


27.07 


10. ,39 


27.03 


10.51 


26.98 


10.63 


26.94 


10.75 


29 


30 
31 


28.01 


10.75 


27.96 


10.87 
11.24 


27.91 


11.00 


27.86 
28.79 


11.12 
11.49 


30 
31 


28.94 


11.11 


28. 8t. 


28.84 


11.36 


32 


29.87 


11.47 


29.82 


11.60 


29.77 


11.73 


29.72 


11.86 


32 


33 


30.81 


11.83 


30.76 


11.96 


30.70 


12.09 


.30.65 


12.23 


33 


34 


31.74 


12.18 


31.69 


12.32 


31.63 


12.46 


31. .58 


12.60 


34 


35 


32.68 


12.54 


32.62 


12.69 


32 . 56 


12.83 


32.51 


12.97 


35 


36 


33.61 


12.90 


33.. 55 


13.05 


33.50 


13.19 


33.44 


13.34 


36 


37 


34.54 


13.26 


34.48 


13.41 


34.43 


13.56 


34.37 


13.71 


37 


33 


35.48 


13.62 


35.42 


13.77 


35.36 


13.93 


35.29 


14.08 


38 


39 


36.41 


13.98 


36 . 35 


14.14 


36.29 


14.29 


36.22 


14.45 


39 


40 
41 


37.34 

33.28 


14.33 


37.28 


14.50 


37.22 


14.66 


37.15 


14.82 


40 
41 


14.69 


38.21 


14.86 


38.15 


15.03 


38.08 


15.19 


42 


39.21 


15.05 


39.14 


15.22 


39.08 


15.39 


39.01 


15.56 


42 


43 


40.14 


15.41 


40.08 


15. .58 


40.01 


15.76 


39.94 


15.93 


43 


4-1 


41.08 


15.77 


41.01 


15.95 


40.94 


.16.13 


40.87 


16.30 


44 


45 


42.01 


16.13 


41.94 


16.31 


41.87 


16.49 


41.80 


16.68 


45 


46 


42.94 


16.48 


42.87 


10.67 


42.80 


16.86 


42.73 


17.05 


46 


47 


43. S8 


16.84 


43.80 


17.03 


43.73 


17.23 


43.65 


17.42 


47 


48 


44.81 


17.20 


44.74 


17.40 


44.66 


17.59 


44.58 


17.79 


48 


49 


45.75 


17. .56 


45.67 


17.76 


45.59 


17.96 


45.51 


18.16 


49 


50^ 


40.68 


17.92 


46 ^6£ 


18.12 


46.52 


18.33 


46.44 
Dep. 

68i 


18.53 


_50 

1 


.2 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Lat. 
Deg. 


69 


Deg. 


68^ 


Deg 


1 08i 


Deg. 



TKAVEKSE TABLE. 



45 



5 

9 

'51 


21 Oeg. 


2Ii Deg. 


21i Deg. 


211 De.. 


1 


Lat. 

47.61 


Dep. 


Lat. 1 Dep. 
47.53 ! 18.48 


Lat. 1 Dep. 


Lat. 


Dep. 




18.28 


47.45 j 18.69 


47.37 


18.90 


"51 


52 


4S.55 i 18.64 


48.46 ! 18.85 


48. .38 19.06 


48.30 


19.27 52 


53 


49.48 i 18.99 1 


49.40 ; 19.21 


49.31 |19 42 


49.23 


19.64 ' 53 


54 


50.41 i 19.35 1 


50.33 19.57 


50.24 ! 19.79 


50.16 


20.01 .5' 


55 


51.35 ; 19.71 ! 


51.26 ! 19.93 


51.17 ^20.16 


51.08 


20.38; 5. 


58 


52 28 [20.07 


.52.19 20.30 


.52. 10 120.52 


.52.01 


20.75 1 Ri^.l 


57 


53 21 20.43 


53.12 20.66 


.53.03 20.89 


52 . 94 


21.12 1 57! 


58 


54.15 120.79 


.54.06 ! 21.02 


53.96 121.26 


.53.87 


21.49 


58 


59 


55.08 i 21.14 


54.99 '21.38 


54.89 21.62 


.54.80 


21.86 


59 


CO 
61 


56.01 
56.95- 


21.50' 


55.92 ! 21.75 


55.83 


21.99 


55.73 


22.23 


60 
61 


21.86 


56.85 i22.11 


5G.76 


22.36 


56.66 


22.60 


fi2 


57.88 


22.22: 


57.78 22.47 


57.69 


22 . 72 


57.59 


22.97 


62 


63 


58.82 


22.58 : 


58.72 


22.83 


58 . 62 


23.09 ! .58 . .52 


23.35' 63 


64 


.59.75 


22.94 


59.65 


23.20 


59.55 


23.46 159.44 


23 . 72 64 


65 


60.68 


23.29 


60.. 58 


23.56 


60.48 


23.82 160.37 


24.09 65 


6G 


61.62 


23.65-01.51 


23.92 


61.41 


24.19 ji 61.30 


24.46 ' 66 


67 


62.55 124.01 1 62.44 


24.28 


62.34 


24.56 1162.23 


24.33 ; 67 


68 


63.48 124.37 163.38 


24.65 


63.27 


24.92 f|63.16 


25.20 63 


69 


64.42 124.73!: 64.31 125.01 


64.20 


25.29 <\ 64.09 


25.57 1 69 


70 
'71 


65.35 


25.09; 65.24 25.37 


65.13 25.66 '65.02 


25.94 


70 


6h.28 


25.44 1 66.17 


25.73 


66.06 


26.02: 65.95 


26.31 


71 


72 


67.22 125.80 


67.10 


26.10 


66.99 


26.39 1, 66.87 


26.68 i 72 


73 68.15 '26.16 


68.04 


26.46 


67.92 


26.75 !i 67.80 


27.05 1 73 


74 


69.08 


26.52 


68.97 


26.82 


68.85 


27.12 1168.73 


27.42 1 74 


75 


70.02 


26.88 


69.90 


27.18 


69.78 


27.49 i 69.66 


27.79 75 


76 


70.95 


27.24 


70.83 


27.55 


70.71 


27.85 70.59 


28.16 1 76 


77 


71.89 


27.59 


71.76 


27.91 


71.64 


28.22 i! 71.52 


28.53 


77 


78 


72.82 


27.95 


72.70 


28.27 


72.57 


28.59 !i 72.45 


28.90 


78 


79 


73.75 


28.31 


73.63 


28.63 


73.50 


28.95 li 73.38 


29.27 


79 


SO 
-81 


74.69 


28.67 


74.56 
75.49 


29.00 


74.43 


29.32 


74.30 
'75.23 


29.64 


80 


75.62 


29.03 


29.36 


75 . 36 


29.69 


30.02 ! 81 


82 


76.55 


29.39 


76.42 


29 . 72 


76.29 


30.05 ,!76.16 


30 . 39 1 82 


83 


77.49 


29.74 


77.36 


30.08 ll 77.22 


30.42 i! 77.09 


30.76 1 83 


84 


78.42 


30.10 


78.29 


30.44 ii 78. 16 


30.79 


' 78.02 


31.13 1 84 


85 


79.35 


30.46 


79.22 


30.81 


79.09 


31.15 


i 78.95 


31.50 I 85 


86 


80.29 


30.82 


80.15 131.17 


80.02 


31.52 


79.88 


31.87 


86 


87 


81.22 


31.18 


81.08 


31.53 


80.95 


31.89 


80.81 


32.24 


87 


88 


82.16 


31 54 


82.02 


31.89 


81.88 


32.25 


81.74 


32.61 


88 


89 


83.09 


31.89 


82.95 


32.26 


82.81 


32.62 


182.66 


32.98 


89 


90 
91 


84.02 


32.25 


83.88 1 32.62 


83.74 


32.99 


183.59 


33 . 35 


90 
"91 


84.96 [32.61 


■84.81 


32.98 


84.67 


33.35 


,84.52 


33.72 


92 


85.89 


.32.97 


1 85.74 


33.34 


85.60 


33.72 


'85.45 


34.09 


92 


93 


86.82 


33.33 li 86.68 


33.71 


86.-53 


34.08 


186.33 


34.46 


93 


94 


87.76 


33.69 


187.61 


34.07 


187.46 


34.45 


87.31 


34.83 


94 


95 


88.69 


34.04 


88.. 54 


34.43 188.39 


34.82 


i 88.24 


35.20 


95 


96 


89.62! 34.40 


89.47 


34.79 89.32 


35.18 li 89.17 


35.57 


96 


97 


90.56 


34.76 


90.40 35.16 90.25 


35.55 190.09 


35.94 


97 


9S 


91.49 


35.12 


91.34 : 35.52 91.18 135.92 i| 91.02 


36.31 


98 


99 


92.42 


35.48 


92.27 , 35.88 92.11 136.28 i| 91.95 


36.69 ' 99 


100 

■s 
5 


93.36 


35.84 


93.20 36.24 93.04 


36.65 ll 92.88 


37.06 ilOO 


Dop. 


Lat. 


Dep. 1 Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


C3 


69 Deg. 


68J Deg. 


' 68i Deg. 


68J Deg. 



22 



46 



TRAVERSE TABLK. 



3 

55' 


22 


Deg. 


224 Deg. 


22^ 


Deg. 


221 Deg. 


D 
1 

i 


P 


Lai. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.93 


0.37 


0.93 


0.38 


0.92 


0..38 


0.92 


0.39 


2 


1.85 


0.75 


1.85 


0.76 


1.85 


0.77 


1.84 


0.77 


2 


3 


2.78 


1,12 


2.78 


1.14 


2,77 


1.15 


2.77 


1.16 


3 


4 


3.71 


1.50 


3.70 


1.51 


3,70 


1.53 


3.69 


1.55 


4 


5 


4.64 


1.87 


4.63 


1.89 


4,62 


1.91 


4.61 


1.93 


5 


6 


5.56 


2.25 


5.55 


2,27 


5.. 54 


2.30 


5.53 


2 , 32 


6 


7 


6,49 


2.62 


6.48 


2,65 


6.47 


2.68 


6.40 


2.71 


7 


8 


7.42 


3.00 


7.40 


3.03 


7,39 


3,06 


7.38 


3,09 


8 


9 


8.34 


3.37 


8.33 


3.41 


8.31 


3.44 


8.30 


3,48 


9 


10 


9.27 


3.75 


9.26 


3.79 


9 . 24 


3.83 


9.22 


3.87 


10 
if 


11 


10.20 


4.12 


10.18 


4.17 


10.16 


4.211 


10,14 


4,25 


12 1 11.13 


4.50 


11.11 


4.54 


11,09 


4.59 


11.07 


4,64 


12 


13 12.05 


4.87 


12.03 


4.92 


12.01 


4.97 


11.99 


5.03 


13 


14 


12.98 


5.24 


12.96 


5.30 


12.33 


5.36 


12.91 


5.41 


14 


15 


13.91 


5.62 


13.88 


5.08 


13.86 


5.74 


13.83 


5.80 


15 


16 


14, S3 


5.99 


14.81 


6.06 


14,78 


6.12 


14.76 


6.19 


16 


17 


15.76 


6.37 


15.73 


6,44 


15,71 


6.51 


15.68 


6,57 


17 


18 


16,69 


6.74 


16.66 


6.82 


16.63 


6.89 


16.60 


6,96 


18 


19 


17.62 


7.12 


17.59 


7.19 


17.55 


7.27 


17.52 


7,35 


19 


20 
21 


18.54 


7.49 


18.51 


7.57 


18,48 


7.65 


18.44 


7.73 


20 


19.47 


7.87 


19,44 


7.95 


19,40 


8.04 


19.37 


8,12 


21 


22 


20.40 


8.24 


20,36 


8.33 


20.33 


8.42 


20.29 


8.51 


22 


23 


21.33 


8.62 


21,29 


8,71 


21.25 


8.80 


21.21 


8.89 


23 


24 


23.25 


8.99 


22,21 


9,09 


22.17 


9.18 


22.13 


9.28 


24 


25 


23,18 


9.37 


23.14 


9,47 


23.10 


9.57 '123.05 


9.67 


25 


26 


24,11 


9.74 


24.08 


9.84 


24.02 


9.95: 23.98 


10.05 


26 


27 


25.03 


10.11 


24.99 


10.22 


24.94 


10.33 11 24.90 


10.44 


27 


2S 


25.96 


10.49 


25.92 


10.60 


25.87 


10.72 i| 25.82 


10.83 


28 


20 


26.89 


10.86 


26.84 


10.98 


26.79 


11.10 126.74 


11.21 


29 


30 


27.82 


11.24 


27.77 


11.36 


27 . 72 


11.48 


27.67 


11.60 


30 


31 


28.74 


11.61 


28.69 


11.74 


28.64 


11.86 


28.59 


11.99 


31 


32 


29.67 


11.99 


29 . 62 


12.12 


29.56 


12.25 


29,51 


12.37 


32 


33 


00,60 


12.36 


30,54 


12.50 


30.49 


12.63 


30.43 


12.76 


33 


34 


3 1.. 52 


12.74 


31,47 


12.87 


31.41 


13,01 


131.35 


13.15 


34 


35 


32,45 


13,11 


32.39 


13.25 


32.34 


13,39 


32.28 


13.53 


35 


36 


33.38 


13.49 


33.32 


13.63 


33 . 26 


13.78 


33.20 


13.92 


36 


37 


34.31 


13.86 


34.24 


14.01 


34.18 


14,16 


34,12 


14.31 


37 


38 


35.23 


14.24 


35.17 


14.39 


35.11 


14,54 


35.04 


14.70 


38 


39 


36.16 


14.61 


36.10 


14.77 


36.03 


14,92 


35.97 


15.08 


39 


40 


37.09 


14.98 


37.02 


15,15 


36.96 


15.31 


.36.89 


15.47 


40 
41 


41 


38.01 


15.36 


37.95 


15.. 52 


37.88 


15.69 


37.81 


15.86 


42 


38.94 


15.73 


38.87 


15.90 


33.80 


16.07 


38.73 


16.24 


42 


43 


39.87 


16.11 


39.80 


16.28 


39.73 


16.46 


39,65 


16.63 43 1 


44 


40.80 


16.48 


40.72 


16.66 


40 . 65 


16.84 


40.58 


17.02 


44 


45 


41.72 


16.86 


41.65 


17.04 


41. .57 


17.22 


41.. 50 


17.40 


45 


46 


42.65 


17.23 


42 , 57 


17.42 


12.50 


17.60 


42.42 


17.79 


46 


47 


43.58 


17.61 


43,50 


17.80 


43.42 


17.99 


43.34 


18.18 


47 


48 ! 44.50 


17.98 


44.43 


18.18 


44.35 


18.37 


44.27 


18.56 


48 


49 1 45.43 


18.36 


45.35 


18.55 


45.27 


18.75 


45.19 


18.95 


49 


50 


46.36 


18.73 


46.28 


18.93 


46.19 


19,13 


46.11 


19.34 


50 

1 
.2 

Q 


I 
1 

Q 


Dep. 


Lat. 


Dep. 


Lat, 


Dep. 


Lat. 


Dep. 


Lat. 


68 


Dog. 


67J Deg. 


67i 


Deg. 


67i Deg. 



TRAVERSE TABLE. 



4? 



s. 

1 

? 
61 


22 Deg. 


221 Deg. 1 


221 Deg. 

1 


221 Deg. 


1 


Lat. Dep. 
47.29 19.10 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


47.20 


19.31 


47.12 


19.. 52 


47.03 


19.72 ! 


52 


48,21 : 19.48 


48.13 


19.69 


48.04 


19.90 


47.95 


20.11 1 


52 


53 49.14 19.85 


49.05 


20.07 


48.97 


20.28 


48. «8 


20.50 


53 


54 50.07 120.23 


49.93 


20.45 


49.89 


20.66 


49.80 


20.88 


54 


55 ! 51.00 i 30.60 


50.90 ! 


20.83 


.50.81 


21.05 


.50.72 


21.27 j 


5;. 


56 1 51.92 1 20.98 


51.83 1 


21.20 


51.74 


21.43 


51.64 


21.66 


5(j 


57 ,62.85 21.35 


52.76 


21. .58 


52.66 


21.81 


52.. 57 


?.2.04 


67 


58 53.78 1 21.73 


53.68 


21.96 


53.59 


22.20 


.53.49 


22.43 


58 


59 154.70! 22.10 


54.61 


22.34 


.54.51 


22.58 


.54.41 22.82 


69 


60 


55.63 122.48 


55.. 53 


22.72 


55.43 
56 . 36 


22.96 
23.34 


55.33 1 23.20 


60 
61 


61 


56.. 56 1 22.85 


56.47 


23.10 


56.25 


23.. 59 


62 57.49 23.23 


57.38 


23.48 1 


57.28 


23.73 


57.18 


23.98 


62 


63 58.41 23.60 


58.31 


23.85 


58.20 


24.11 


58.10 


24.36 


63 


64 59.34 23.97 


.59.23 


24.23 


59.13 


24.49 


59.02 


24.75 


64 


65 60.27 24.35 


60.16 


24.61 


60.05 


24.87 


59 . 94 


25.14 


65 


66 61.19 24.72 


61.09 


24.99 


60.98 


25.26 


60.87 


25.52 


66 


67 


62.12 25.10 


62.01 


25.37 


61.90 


25.64 


61.79 


25 . 9 1 


67 


68 


63.05! 25.47 


62.94 


25.75 


62.82 


26.02 


62.71 


26.30 


68 


69 


63.98 125.85 


63.86 


26.13 


63 . 75 


26.41 


63.63 


26.68 


69 


70 

71 


64.90 


26.22 


64.79 


26.51 


64.67 
65.60 


26.79 
27.17 


64.55 


27.07 


70 

71 


65.83 


26.60 


65 . 7 1 


26.88 


65.48 


27.46 


72 


66.76 


26.97 


66.64 


27.26 


66 52 


27.55 


66.40 


27.84 


72 


73 


67.68 


27.35 


67.56 


27.64 


67.44 


27 . 94 


67.32 


28.23 


73 


74 


68.61 


27.72 


68.49 


28.02 


68.37 


28.32 


68.24 


28.62 


74 


75 


69.54 


28.10 


69.42 


28.40 


69.29 


28.70 


69.17 


29.00 


75 


76 


70.47 


28.47 


70.34 


28.78 


70.21 


29.08 


70.09 


29.. 39 


76 


77 


71.39 


28.84 


71.27 


29.16 


71.14 


29.47 


71.01 


29.78 


77 


78 


72.. 32 


29 . 22 


72.19 


29.53 


72.06 


29.85 1 71.93 


30.16 


78 


79 


73.25 


29.59 


73.12 


29.91 


72.99 


3). 23 


72.85 


,30.. 55 


79 


80 
81 


74.17 
75.10 


29.97 


74.04 


30.29 
30.67 


73.91 


30.61 


73.78 


30.94 


80 
SI 


30.. 34 


74.97 


74.83 


31.00 


74.70 


31.32 


82 


76.03 


30.72 


75.89 


31.05 


75.76 


31.38 


75.62 


31.71 


82 


83 


76.96 


31.09 


re. 82 


31.43 


76.68 


31.76 


70.54 


32.10 


83 


84 


77.88 


31.47 


77.75 


31.81 


77.61 


32.15 


77.46 


32.48 


84 


85 


78.81 


31.84 


78.67 


.32.19 


78.53 


32.53 


78.39 


32.87 


85 


86 


79.74 


32.22 


79.60 


32.56 


79.45 


32.91 


79.31 


33.26 


86 


87 


80.60 


32.59 


80.. 52 


32 . 94 


80.38 


.33.29 


180.23 


33.64 


87 


88 


81.59 


32.97 


81.45 


33.. 32 


81.30 


33.68 


81.15 


34.03 


88 


89 


82.52 


33.34 


82.37 


33.70 


82.23 


34.06 


182.08 


34.42 


89 


90 
91 


83.45 


33.71 


83.30 


34.08 


83.15 


34.44 


1 83 . 00 


34.80 
35.19 


90 
91 


84.37 


34.09 


34.22 


34.46 


84.07 


34.82 


! 83.92 


92 85.30 


34.46 


85.15 


34.84 


85.00 


35.21 


184.84 


35.58 


92 


93 86. 23 1.34. 84 


86.08 1 35.21 


85.92 


35 . 59 


1 85 . 76 


35.96 


93 


94 87.16 35.21 


87.00 35.59 


86.84 


35.97 


86.69 


36.35 


94 


95 88. 08 1.35. 59 


87.93 35.97 


87.77 


36.35 


87.61 


36.74 


95 


96 89.01 135.96 


88.85 36.35 


88.69 


3">.74 


88.. 53 


37.12 


96 


97 89.94] 36.34 


89.78 36.73 


89.62 37.12 


189.45 


137.51 


1 97 


93 90.86 136.71 


90.70 37.11 


90..54 137.50 


90.38 


1 37.90 


i 98 


99 91.79 137.09 


91.63 37.49 


'91.46 37.89 


:91.30 


38.28 


1 99 


100 


92.72 


37.46 


92.. 55 37.86 


92 .39_j 38.27 


; 92.22 


38.6^ 


, 100 

! §• 

1 c 

1 5 




Dep. 


Lat. 


Dep. j Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


5 

5 


68 Deg. 


671 Deg. 


C7i Deg. 


67J Deer. 



48 



TRAVKKSE TABLE, 



o 


23 Deg. 


23i Deg. 


23^ Deg. 


231 Deg. 


r 


Lat. 


Dcp. 


Lat. 


Dcp. 


Lat. 


Dep, 


L«. 


Dep. 

0.40 


1 


0.92 


0.39 


0.92 


0.39 


0.92 


0.40 


0.92 


2 


1.84 


0.78 


1.84 


0.79 


1,83 


0.80 


1.83 0.81 


2 


3 


2.76 


1.17 


2.76 


1.18 


2,75 


1.20 


2.75' 1.21 


3 


4 


3.68 


1.56 


3.68 


1.58 


3.67 


1.59 


3.66 1 1.61 


1 


5 


4.60 


1.95 


4.59 


1.97 


4.. 59 


1.99 


4.58! 2.01 


5 


6 


5.52 


2.34 


5.51 


2., 37 


5.50 


2.39 


5.491 2.42 


6 


7 


6.44 


2.74 


6.43 


2.76 


6.42 


2! 79 


6.41 1 2.82 


7 


8 


7.36 


3.13 


7.35 


3.16 


7.34 


3.19 


7,32 


3.22 


8 


9 


8.28 


3.52 


8.27 


3.55 


8.25 


3.59 


8.24 


3,62 


9 


10 


9.20 


3.91 


9.19 
10.11 


3.95 
'4.34 


9.17 
10.09 


3.99 
4.39 


9.15 
10.07 


4.03 
4.43 


10 
11 


11 i 10.13 


4.30 


12 111.05 


4.69 


11.03 


4.74 


11.00 


4.78 


10.98 


4.83 


12 


13 11.97 


5.08 


11.94 


5.13 


11.92 


5.18 


11,90 


5.24 


13 


14 i 12.89 


5.47 


12.86 


5.. 53 


12.84 


5.58 


12,81 


5.64 


14 


15 


13.81 


5.86 


13.78 


5.92 


13.76 


5.98 


13.73 


6,04 


15 


16 


14.73 


6.25 


14.70 


6.32 


14.67 


6.38 


14.64 


6.44 


16 


17 


15.65 


6.64 


15.62 


fi.71 


15.59 


0.78 


15.. 56 


6.85 


17 


.18 


16.57 


7.03 


16., 54 


7.11 


10.51 


7.18 


16.48 


7.25 


18 


19 


17,49 


7.42 


17.46 


7., 50 


17.42 


7,58 


17.39 


7.65 


19 


20 
21 


18.41 


7.81 


18.38 


7.89 


18.. 34 


7.97 


18.31 


8.05 


20 

~21 


19.33 


8.21 


19.29 


8.29 


19.2-^ 


8.37 


19.22 


8.46 


22 


20.25 


8.60 


20.21 


8.68 


20.18 


8.77 


20,14 


8.86 


22 


23 '21.17 


8.99 


21.13 


0.08 


21.09 


9.17 


21.05 


9.26 


23 


24 '22.09 


9.?8 


22.05 


9.47, 


22.01 


9.. 57 


21.97 


9.67 


24 


25 123.01 


9.77 


22.97 


9.87 


22.93 


9.97 


22.88 


10.07 


25 


26 23.93 


10.16 


23.89 


10.26 


23.84 


10.37 


23.80 


10.47 


26 


27 


24.85 


10.. 55 


24.81 


10.66 


24.76 


10.77 


24,71 


10.87 


27 


28 


25.77 


10.94 


25 . 73 


11.05 


25.68 


11,16 


25 . 63 


11.28 


28 


29 


26.69 


11.33 


26.64 


11.45 


26.. 59 


11.56 


26.. 54 


11.68 


29 


30 
31 


27.62 
28.54 


11.72 


27.. 56 


11.84 


27.51 

28.43 


11.96 
12.36 


27 . 46 


12.08 


30 


12.11 


28.48 


12.24 


28.37 


12.49 


31 


32 


29.46 


12.. 50 


129.40 


12.63 


29 . 35 


12.76 


29.29 


12.89 


32 


33 


30 . 38 


12.89 


30.32 


13.03 


30.26 


13.16 


30.21 


13.29 


33 


34 


31.30 


13.28 


31.24 


13.42 


31.18 


13., 56 


31.12 


13.69 


34 


35 


32.22 


13.68 


32.16 


13.82 


32.10 


13.96 


32.04 


14.10 


35 


36 


33.14 


14.07 


33.08 


14.21 


33.01 


14.. 35 


32.95 


14.. 50 


36 


37 


34.06 


14.46 


34.00 


14.61 


33 . 93 


14.75 


33.87 


14.90 


37 


38 


34.98 


14.85 


34.91 


15.00 


34.85, 15.15 


34.78 


15.30 


38 


39 


35.90 


15.24 


35.83 


15.39 


35.77 


15.. 55 


35.70 


15.71 


39 


40 
41 


36.82 
37.74 


15.63 


36.75 
37 . 67 


15.79 
16.18 


36 . 68 

37 . 60 


15.95 


36.61 
"37.-53 


16.11 
16., 51 


40 
41 


16.02 


16.35 


42 


38.66 


16.41 


38.59 


16.58 


38 . 52 


16.75 


38.44 


16.92 


42 


43 


39.58 


16.80 


39.51 


16.97 


39.43 


17.15 


39.36 


17.32 


43 


44 1 40.50 


17.19 


40.43 


17.37 


40 . 35 


17. .54 


40.27 


17.72 


44 


45 141.42 


17. .58 


41.35 1 17.76 


41.27 


17.94 


41.19 


18.12 


45 


46 ' 42.. 34 


17.97 


42.26^ 18.16 


42.18 


18.34 


142.10 


18.53 


46 


47 43 . 26 


18.36 


43.18 18. .55 


43. 10 


18.74 


143.02 


18.93 


47 


48 44.18 


18.76 


44.10 18.95 


44.02 : 19.14 


43.93 


19.33 


48 


49 45.10 


19.15 1145.02 19.34 


44.94 i 19,54 


44.85 


1'».73 


49 


50 46.03 


1 19. .54 45.94 19.74 


45.85 


19 .94 


: 45 . 77 


20.14 


50 

1 


i 


' Dep. 


Lat. Dep. j Lat. 


Dcp. 


Lat, Ij Drp. 


Lat. 




67 


Dog jl 661 Deg. 


66i Deg, 1 66ii Dog. 



TRAVERSE TA.ULE. 



2 


23 Deff. 


23i Deg. 


23| Deg, 


231 
Lat. 


Deg. 




Lat. 


Dep. 


Lat. 


Dep. 


Lat, 


Dep. 


Dep. 


46.95 


19.93 


46.86 


20. i3 


46 . 77 


20.34 


46.68 20.. 54 


61 


52 


47.87 


20.32 


47.78 


20 . 53 


47.69 


20.73 


47,60 20.94 , 52j 


53 


48.79 


20,71 


48.70 


20.92 


48.60 


21.13 


48.51 21.35 53 


54 


49.71 


21.10 


49.61 


21.52 


49.52 


21.53 


49.43 [21.75 ! 54] 


55 


50.63 


21.49 


50.53 


21.71 


50.44 121.93 


50,34 


22.15 


55 


56 


51.. 55 


21.88 


51,45 


22.11 


51.36 ! 22.33 


51,26 


22.55 


56 


57 


52.47 


22.27 


52.37 


22.50 


52.27 


22.73 


52.17 


22.96 


57 


5S 


53.39 


22.66 


53.29 


22.90 


53.19 


23.13 


53.09 


23.36 


58 


59 


54.31 


23.05 


54.21 


23.29 


54.11 


23.53 


.54.00 


23.76 


59 


60 
61 


55 . 23 


23.44 


55.13 


23.63 


55.02 


23.92 


54.92 


24,16 


60 


56.15 


23.83 


56.05 


24. OS 


55.94 


24.32 


.55.83 124,57 j 61 1 


62 


57.07 


24.23 


56.97 


24.47 


.56.86 


24.72 


.56.75 24.97 1 62] 


63 


57.99 


24.62 


57.88 


24.87 


57.77 


25.12 


.57.66 


25 . 37 63 


64 


58.91 


25.01 


58.80 


25.20 


.58.69 


25.52 


58.58 


25,73 64 


65 


59.83 


25.40 


59 . 72 


25 . 66 


59.61 


25 . 92 


59.. 50 


26.18 65 


66 


60.75 


25.79 


60.64 


26.05 


60 . 53 


26.32 


60.41 


26.. 58 1 66 


67 


61.67 


26.18 


61.56 


20.45 


61.44 


20.72 


61.33 


26.93 


67 


6S 


62.59 


26.57 


62.48 


26.84 


62.36 


27.11 


62.24 


27.39 


68 


69 


63.51 


26.98 


63.40 


27.24 


63.28 


27.51 


63.16 


27.79 


89 


70 
71 


64.44 
65.36 


27.35 


64.32 


27.63 


64.19 


27.91 


64.07 


23.19 
28.59 


70 
71 


27.74 


65.23 


28.03 


65 . 1 1 


23.31 


64.99 


72 


66.28 


28.13. 


66.15 


28.42 


66.03 


23.71 


65.90 


29.00 


72 


73 


67.20 


28.. 52 


67.07 


23.82 


63.95 


29.11 


66.82 


29.40 


73 


74 


68.12 


28.91 


67.99 


29.21 


67.86 


29.51 


67.73 


29.30 


74 


75 


69.04 


29.30 


68.91 


29,61 


68,78 


29.91 


68.65 


30.21 


75 


76 


69.99 


29.70 


69.83 


30.00 


69.70 


30.30 


69.-56 


30.61 


76 


77 


70.88 


30.09 


70 . 75 


30,40 


70.61 


30.70 


70.43 


31.01 


77 


78 


71.80 


30,48 


^.67 


30,79 


71.53 


31.10 


71.39 


31.41 


73 


79 


72.72 


30.87 


72.53 


31.18 


72.45 


31.50 


72.31 


31.82 


79 


80 
81 


73.64 


31.26 


73.50 


31.58 


73.36 


31.90 


73.32 


32.22 


30 
81 


74.. 56 


31.65 


74.42 


31.97 


74.23 


32.30 


74.14 


.32.62 


82 


75.48 


32.04 


75.34 


32.37 


75.20 


32.70 


75.06 


33.03 


S3 


83 


76.40 


32.43 


76.26 


32 . 76 


76.12 


33.10 


75.97 


33.43 


33 


84 


77.32 


32.82 


77.13 


33,16 


77.03 


33.49 


76,89 


33.83 


34 


85 


78.24 


33.21 


78.10 


33.55 


77.95 


33.89 


77,80 


34.23 


85 


86 


79.16 


33.60 


79.02 


33.95 


73.87 


34.29 


78 . 72 


34.64 


86 


87 


80.08 


33.99 


79.93 


34.34 


79.78 


34.69 


79 . 63 


35.04 


87 


83 


81.00 


34.33 


80.85 


34.74 


80.70 


35.09 


80.55 


35.44 


88 


89 


81.92 


34.78 


81.77 


35,13 


81.62 


35.49 


81.46 


35.84 


89 


90 
91 


82.85 


35,17 


82.69 


35.53 


82.54 


35.89 


82.33 


36.25 


90 
9! 


83.77 


35.56 


83.61 


35.92 


83.45 


36.29 


83.29 


36.65 


93 


84.69 


35.95 


84.53 


36.33 


84.37 135.63 


84.21 


37.05 92 


93 


85.61 


36.34 


85.45 


36,71 


85.29: 37.08 


85,12 


37.46 93 


94 


86. .53 36.73 


86.37 


37.11 


86.20' 37.48 


86.04 


37.86 '■ 94 


95 


87.45 37.12 


87.29 


37.50 


87.12 37.88 


86.95 


33.26 1 95 


96 


88.37 i 37.51 


88.20 


37.90 


88.04! 33.28 


87.37 


38 . 66 


96 


97 


89.29 1 37.90 


89.12 


33.29 


88.95 .38.68 


88.79 


39.07 


97 


98 


90.21 t 38.29 


90.04 


33.68 


89.87 39.03 


89.70 


39.47 


98 


99 


91.13 •' 33.68 


90.96 


39.03 


90.79 39.48 


90.62 


.39.87 


99 


100 

1 

a 


92.05 .39.07 
Dep. Lat. 


91.88 


39.47 


91.71 |39.87 


91.53 


40,27 


100 


Dep. 


Lat, 


Dep. 1 Lat. 


Dep 


Lat. 


1 

3 


67 Deg. 


66| Deg. 


66i Deg. 


6Gk Deg. 



60 



TRAVERSE TABLE. 



'~1 


24 


Deg. 


24i Deg. 


241 


Deg. 


241 Deg. 


O 

1 
p 

1 


Lat. 
0.91 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.41 


0.91 


-0741 


0.91 


0.41 


0.91 


0.42 


2 


1.83 


0.81 


1.82 


0.82 


1.82 


0.83 


1.82 


0.84 


2 


3 


2.74 


1.22 


2.74 


1.23 


2.73 


1.24 


2.72 


1.26 


3 


4 


3.65 


1.63 


3.65 


1.04 


3.64 


1.66 


3.63 


1.67 


4 


5 


4.57 


2.03 


4.56 


2.05 


4.55 


2.07 


4.54 


2.09 


5 


6 


5.48 


2.44 


5.47 


2.46 


5.46 


2.49 


5.45 


2.51 


6 


7 


6.39 


2.85 


6.38 


2.87 


6.37 


2.90 


6.36 


2.93 


7 


8 


7.31 


3.25 


7.29 


3.29 


7.28 


3.32 


7.27 


3.35 


8 


9 


8.22 


3.66 


8.21 


3.70 


8.19 


3.73 


8.17 


3.77 


9 


10 
11 


9.14 
10.05 


4.07 
4.47 


9.12 


4.11 


9.10 


4.15 


9.08 


4.19 


10 
11 


10.03 


4.52 


10.01 


4.56 


9.99 


4.61 


12 


10.96 


4.88 


10.94 


4.93 


10.92 


4.98 


10.90 


5.02 


12 


13 


11.88 


5.29 


11.85 


5.34 


11.83 


5.39 


11.81 


5.44 


13 


14 


12.79 


5.69 


12.76 


5.75 


12.74 


5.81 


12.71 


5.86 


14 


15 


13.70 


6.10 


13.08 


6.16 


13.65 


6.22 


13.62 


6.28 


15 


16 


14.62 


6.51 


14.. 59 


6.57 


14.56 


6.64 


14.53 


6.70 


16 


17 


15.. 53 


6.92 


15.50 


6.98 


15.47 


7.05 


15.44 


7.12 


17 


18 


16.44 


7.32 


16.41 


7.39 


16.38 


7.46 


16.35 


7.. 54 


18 


19 


/7.36 


7.73 


17.32 


7.80 


17.29 


7.88 


17.25 


7.95 


19 


20 
21 


18.27 


8.13 


18.24 


8.21 


18.20 


8.29 


18.16 


8.37 


20 
21 


19.18 


8.54 


19.15 


8.63 


19.11 


8.71 


19.07" 


8.79 


22 


20.10 


8.95 


20.06 


9.04 


20.02 


9.12 


19.98 


9.21 


22 


23 


21.01 


9.35 


20.97 


9.45 


20.93 


9.54 


20.89 


9.63 


23 


24 


21.93 


9.76 


21.88 


9.86 


21.84 


9.95 


21.80 


10.05 


24 


25 


22.84 


10.17 


22.79 


10.27 


22.75 


10.37 


22.70 


10.47 


25 


26 


23 . 75 


10.. 58 


23.71 


10.68 


23.66 


10.78 


23.61 


10.89 


26 


27 


24.67 


10.98 


24.62 


11.09 


24.57 


11.20 


24.52 


11. .30 


27 


28 


25.. 58 


11.39 


25.. 53 


11. .50 


25.48 


11.61 


26.43 


11.72 


28 


29 


26.49 


11.80 


26.44 


11.91 


26.39 


12.03 


26.34 


12.14 


29 


30 
31 


27.41 


12.20 


27.35 


12.32 


27.30 


12.44 


27.24 


12., 56 


30 
31 


28,32 


12.61 


28.26 


12.73 


28.21 


12.86 


28.15 


12.98 


32 


29.23 


13.02 


29.18 


13.14 


29.12 


13.27 


29.06 


13.40 


32 


33 


30,15 


13.42 


30.09 


13.55 


30.03 


13.68 


29.97 


13.82 


33 


34 


31.06 


13.83 


31.00 


13.96 


30.94 


14.10 


30.88 


14.23 


34 


35 


31.97 


14.24 


31.91 


14.38 


31.85 


14.51 


31.78 


14.65 


35 


36 


32.89 


14.64 


32.82 


14.79 


32.76 


14.93 


32.69 


15.07 


36 


37 


33.80 


15.05 


33.74 


15.20 


33.67 


15.34 


lf)3.60 


15.49 


37 


38 


34.71 


15.46 


34.65 


15.61 


34.58 


15.70 


.34.51 


15.91 


38 


39 


35.63 


15.86 


35.56 


16.02 


.35.49 


16.17 


35.42 


16.33 


39 


40 


36.54 


16.27 


36.47 


16.43 


36.40 


16.59 


36.33 


16.75 


40 


41 


37.46 


16.68 


37.38 


16;84 


37.31 


17.00 


37.23 


17.16 


41 


42 


38 . 37 


17.08 


38 . 29 


17.25 


38.22 


17.42 


38.14 


17.58 


42 


43 


39.28 


17.49 


39.21 


17.60 


39.13 


17.83 


.39.05 


18.00 


43 


44 


40.20 


17.90 


40.12 


18.07 


40.04 


18.25 


39.96 


18.42 


44 


45 


41.11 


18.30 


41.03 


18.48 


40.95 


18.66 


40.87 


18.84 


45 


46 


42.02 


18.71 


41.94 


18.89 


41.86 


19.08 


41.77 


19.26 


46 


47 


42.94 


19.12 


42.85 


19.30 


42 . 77 


19.49 


42.68 


19.68 


47 


48 


43.85 


19.52 


43.70 


19.71 


43.68 


19.91 


43.. 59 


20.10 


48 


49 


44.78 


19.93 


4^4.68 


20.13 


44.. 59 


20.32 


44.50 


20.51 


49 


50 

g 

c 
a 


45.68 


20.34 


45.59 


20.. 54 


45.50 


20.73 


45.41 


20.93 


50 


Dep. 


Lat. 


Dep. 


Lntr 


Dep. 

651 


Lat. 
Deg. 


Dep. 


Lat. 


S 


66 1 


)eg. 


65| Deg. 


65^ Deg. 



TRAVEUSE TABLE. 



51 



2 


24 Deg. 




Lat. 


Dep. 1 


51 
52 
53 
54 
55 


46.59 
47 . .50 

48.42 
49.33 
.50.24 


20.74; 
21.15 i 
21.56 
21.96 
22.37 



24i Deg. 



Lat, I Dep. 



77 
7S 
79 

81 
82 
S3 
84 
85 
85 
87 
88 
89 
9J) 
91 
92 
93 
94 
95 
I 96 
97 
98 
99 
100 



.07 23 
.99 , 23 
.90 24 

■ll\^ 
.73 24" 
.64 25 
..55 25 
,47 I 26 
.33 I 26 
,29 25 



46, 
47, 

48, 
49. 
50, 

78,151, 
18 ; 51. 
59 1.52, 
00 .53. 
.40 |l54, 
81 ii 55, 
22 n 56, 
62 ■ 57. 
03 Us. 
44 59, 
ij.f ! fill 



.84 ' 60 
. 25 I 6 1 



.21 27 

.12 27.66 ; 62 

,03 23.06 I 62 

,95 23. 



86 23 
78 29 
69 ' 29 
60 30 
52 30 
43 30 
34 31 
26 31 
17 i 32 
OS 32 



47 63. 
83 :j 64. 

65. 

66. 

67. 



20.95 
21.36 
21.77 
22.18 
22.. 59 
23.00 
23.41 
23.82 
24.23 
24.64 



24i Deg. 



Lat. Dep, 



00 132, 
91 I 33, 

82 I 33, 
74 3t, 
65 34, 
56 134, 
48 35. 
39 35, 
31 36, 
22 36. 



13 37 
05 37 
96 , 37 
87 ' 33 
79 , .38 
70 :39 
61 ; 39 
53 '39 
44 40 
35 '40 



25.05 
25.46 
25.88 
26.29 
26.70 
27.11 
27.52 
37.93 
28.34 
23.75 



29.16 
29.57 
29.98 
30.39 
30.80 
31.21 
31.63 
32.04 
32.45 
32.86 



35 

76 
17 
57 
98 
39 
79 
20 

01 

42 'i 83, 
83 : 84. 
23'! 85, 
64 I 86. 
05 : 87, 
45 , 88 
86 ! 89, 
27 J 90, 
67 I 91, 



33.27 
33.68 
34.09 
34.. 50 
34.91 
35.32 
35 . 73 
36.14 
36.55 
36.96 



97 ,37.38 
88 37.79 
79 ; 38.20 
71 33.61 
62 39.02 
53 ! 39.43 
44 139.84 
35 40.2.5 
26 40.66 
18 41.07 



Dep, Lat, I Dep. Lat. 



66De2 



65| Deg, 



46.41 
47.32 
48.23 
49.14 
50.05 
50.96 
51.87 
.52.78 
53.69 
54.60 



55.51 
56.42 
57.33 
.58.24 
59.15 
60.06 
60.97 
61.88 
62.79 
63.70 



64.61 
65.52 
66.43 
67.34 

68.25 
69.16 
70.07 
70.98 

7 1. 89 
72.80 



73.71 
74.62 
75.. 53 
76.44 
77.35 
78 26 
79.17 
80.08 
80 99 
81.90 
82.81 
83.72 
84.63 
85.54 
86.45:39 
87.36 ! 39 
88.27 140 
89.18 40 
90.09 141 
91.00 41, 



24J Deg. 



Lat. Dep. 



46.32 
47.22 
48.13 
49.04 
49 . 95 
50.86 
51.76 
52.67 
53.58 
54.49 



55.40 
56.30 
57.21 
.58.12 
59.03 
59.94 
60.85 
61.75 
62.66 
63.57 



Dep. Lat. 



65* Deg. 



64.43 
65.39 
66.29 
67.20 
68.11 
69.02 
69.93 
70.84 
71.74 
72.65 



i 73 . 56 
74.47 
75.38 
76.28 
77.19 
78.10 
79.01 
i 79.92 
80.82 
:81.73 
i 82 . 64 
83 . 55 
84.40 
185.37 
186.27 
187.18 
88.09 
89.00 
89.91 
90,81 



21.35 
21.77 
22.19 
22.61 
23.03 
23.44 
23.86 
24.28 
24.70 
25.12 
25 . 54 
25.96 
28.38 
26.79 
27.21 
27.63 
28.05 
28.47 
28.89 
29.31 
29.72 
30.14 
30.. 56 
30.98 
31.40 
31.82 
32.24 
32.66 
33.07 
.33.49 



33.91 
34.33 

34.75 
35.17 
35.59 
36.00 
36.42 
36.84 
37 26 
37.68 



33.10 
38.. 52 
38.94 
39.35 
39.77 
40.19 
40.61 
41,03 
41.45 
41,87 



Dep. Lat 



65^ Deg. 



S2 






TRAVERSE TABLE. 












25 


Deg. 


25i Deg. 


25hDeg. 


251 Deg. 


T 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.91 


0.42 


o.so 


0.43 


0.90 


0,43 


0.90 


0.43 


2 


l.Sl 


0.85 


1,81 


0.85 


1.81 


0,86 


1.80 


0.87 


2 




3 


2.72 


1.27 


2.71 


1.28 


2.71 


1,29 


2.70 


1.30 


3 




4 


3.63 


1.69 


3.62 


1.71 


3.61 


1.72 


3.60 


1,74 


4 




5 


4.53 


2.11 


4.52 


2.13 


4.51 


2.15 


4.50 


2.17 


5 




6 


5.44 


2.54 


5.43 


2.. 56 


5,42 


2,. 58 


5.40 


2,61 


6 




7 


6.34 


2.96 


0..33 


2,99 


6,32 


3.01 


6.30 


3.04 


7 




8 


7.25 


3.38 


7.24 


3,41 


7,22 


3.44 


7.21 


3. 48 


8 




9 


8.16 


3.80 


8,14 


3.84 


8.12 


3.87 


8.11 


3.91 


9 




10 


9.06 


4.23 


9,04 


4.27 


9.03 
9.93 


4.31 


9.01 


4.34 

4.78 


10 
11 




11 


9.97 


4.65 


9,95 


4.69 


4.74 


9.91 


12 


10.88 


5.07 


10,85 


5.12 


10.83 


5.17 


10.81 


5.21 






13 1 11.78 


5.49 


11,70 


5,55 


11.73 


5.60 


11.71 


5.65 


13 




14 12. b9 


5.92 


12.66 


5.97 


1:^.64 


6.03 


12.61 


6.08 


14 




1.5 1 13.59 


6.34 


13.57 


6.40 


13.54 


6.46 


13.51 


6., 52 


15 




IH j 14. ."50 


6.76 


14.47 


6.83 


14.44 


6.89 


14.41 


6.95 


16 




17 15.41 


7.18 


15.38 


7.25 


15.34 


7.32 


15.31 


7.39 


17 




18 16.31 


7.61 


16.28 


7.68 


16.25 


7.75 


16.21 


7.82 


18 




19 


17.22 


8.03 


17.18 


8.10 


17.15 


8.18 


17.11 


8,25 


19 




20 

21 


18.13 
19.03 


8.45 


18.09 


8.53 


18.05 


8.61 


18.01 
18.91 


8.69 
9.12 


20 
21 




8.87 


18r99 


8.96 


18.95 


-9:04" 




19.94 


9.30 


19.90 


9. 33 


19.86 


9.47 


19.82 


9.56 


22 




23 


20.85 


9.72 1 


20.80 


9.81 


20.76 


9,90 


20.72 


9.99 


23 




24 


21.75 


10.14 


21.71 


10.24 


21.66 


10. ,33 


21.62 


10.43 


24 




25 


22.66 


10. .57 


22.61 


10.66 


22.56 


10.76 


22.52 


10.86 


25 




20 


23.56 


10.99 


23.52 


11.09 


23.47 


11.19 


23.42 


11.30 26 




27 


24.47 


11.41 


24.42 


11.52 


24.37 


11.62 


24.32 


11,73 


27 




28 


25.38 


11.83 


25.32 


11.94 


25.27 


12.05 


25.22 


12,16 


28 




29 


26.28 


12.26 


26,23 


12.37 


26.17 


12. 4S 


26.12 


12.60 


29 




30 


27.19 


12.68 


27,13 


12.80 


27.08 


12.92 


27.02 


13.03 


30 




31 


28.10 


13.10 


28.04 


13.22 


27.98 


13.35 1 


27.92 


13.47 


31 




32 


29.00 


13.52 


28.94 


13.65 


28.88 


13.78 


28.82 


13.90 


32 




33 


29.91 


13.95 


29.85 


14.08 


29.79 


14.21 


29.72 


14.34 


33 




34 


30.81 


14.37 


30.75 


14.. 50 


30.69 


14.64 


.30.62 


14.77 


.^4 




:iF 


31.72 


14.79 


31.66 


14.93 


31.59 


15.07 


31,. 52 


15.21 


35 




3f. 


32.63 


15.21 


32.56 


15,36 


32.49 


15.50 


32,43 


15.64 


36 




37 


33.53 


15.64 


33.46 


15,78 


33.40 


15.93 


33.33 


16.07 


37 




38 


34.44 


16.06 


34.37 


16.21 


.34.30 


16.36 


34,23 


16.51 


38 




39 


.35.35 


16.48 


35.27 


16.64 


35.20 


16.79 


35,13 


16.94 


39 




40 3fi.25 


16.90 


36.18 


17.06 


36.10 


17.22 


.36.03 


17.38 


40 




41 


37.16 


17.33 


37.08 


17.49 


37.01 


17.65 


36,93 


17.81 


41 




42 


38,06 


17.75 


37.99 


17.92 


37.91 


18.08 


37,83 


18.25 


42 




43 


38.97 


18.17 


38,89 


18.34 


38.81 


18.51 


38.73 


18.68 


43 




44 


39.88 


18.60 


39,80 


18.77 


39.71 


18.94 


.39,63 


19.12 


44 




45 


40.78 


19.02 


40,70 


19.20 


40,62 


19.37 


40,. 53 


19.. 55 


45 




46 


41.69 


19.44 


41,60 


19.62 


41,. 52 


19.80 


41.43 


19.98 


46 




47 


42.60 


19.86 


42.51 


20.05 


42,42 


20.23 


42.33 


20.42 


47 




48 


43.50 


20,29 


43,41 


20.48 


43,32 


20.66 


43.23 


20.85 


48 




49 


44.41 


20,71 


44.32 


20.90 


44.23 


21.10 


44.13 


21.29 


49 




60 


45.32 


21.13 


45.22 


21.33 


45.13 


21,53 


45.03 


21.72 


50 




j Distance.! 


Dep. 


Lat. 


Dep, 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


1 



65 


Deg. 


64| Deg. 


64i Dog. 


64i Deg. 



TRAVERSE TAT!I,E. 



53 



i 


25 Deg. 


25i Deg, 


25 i Deg. 


231 Deg. 


s 
Id 


Lat. 


Dep. 


Lat. 
46.13 


Dep, 


Lat. 


Dep. 


Lat. 


Dep, 


46.22 


21.55 


21.75 


46.03 


21.90 


45.94 


"22TT0" 


52 


47.13 


21.98 


47,03 


22.18 


46.93 


22.39 


40.84 


22.. 59 


52 


53 


48.03 


22.40 


47,94 


22.61 


47.84 


22.82 


47,74 


23.03 


53 


54 


48.94 


22.82 


48.84 


23.03 


48,74 


23.25 


48.64 


23.40 


54 


55 


49.85 


23.24 


49.74 


23.46 


49.64 


23.68 


49.-54 


23 . 89 


55 


56 


50 . 75 


23,67 


50.05 


23.89 


50.. 54 


24 . 1 1 


.50.44 


24.. 33 


50 


57 


51.66 


24.09 


51.55 


24,31 


51,45 


24.54 


51.34 


24.70 


57 


58 


52 . 57 


24.51 


52.46 


24,74 


52,35 


24.97 


.52.24 


25.20 


58 


59 


.53.47 


24.93 


53.30 


25,17 


53,25 


25.40 


53.14 


25 . 63 


59 


60 
PI 


.54.38 


25.36 


54.27 


25.59 


.54.16 


25.83 


54.04 


26.07 


00 
01 


.55.28 


25,78 


55.17 


26.02 


55.00 


26.20 


54.94 1 26.50 


02 


.56.19 


26.20 


.56,08 


26,45 


55.96 


a<-\pj 


55,8 i •ZF.9k 


6? 


63 


57.10 


26.62 


.56.98 


26.87 


56,80 


^-7 12 


;.0 . 7'1 


'.7 .J7, G3l 


64 


.58.00 


27.05 


.57.89 


27.30 


.57.77 


27.55 


-57.64 


27.80 


64 


65 


,58.91 


27,47 


58.79 


27.73 


58 . 07 


27.98 


.58.. 55 


28.24 


65 


66 


.59.82 


27.89 


59.69 


28.15 


59.57 


28.41 


59.45 


28.07 


66 


67 


60 . 72 


28. 32. 


60.60 


28.58 


00.47 


28.84 


60.35 


29.11 


67 


68 


61.63 


28.74 


61.50 


29.01 


01.38 


29.27 


61.25 


29.. 54 


68 


69 


62.-54 


29.10 


02.41 


29.43 


02.28 


29.71 


62.15 


29.98 


69 


70 
"71 


63.44 


29.58 


63,31 


29.80 


63.18 
64.08 


30.14 


03.05 


30.41 
30.85 


70 

71 


64.35 


30.01 


64,22 


30,29 


30.. 57 


63.95 


72 


65.25 


30.43 


65,12 


30.71 


64.90 


31.00 


64.85 


31.28 


72 


73 


66.16 


30,85 


66.03 


31.14 


65.89 


31.43 


65.75 


31,71 


73 


74 


67.07 


31.27 


60.93 


31. .57 


66.79 


31.86 


60.65 


32.15 


74 


75 


67.97 


31.70 


07.83 


31.99 


67,09 


32.29 


67.. 55 


.32.58 


75 


76 


68.88 


32.12 


08.74 


32.42 


68,60 


32.72 


68.45 


33.02 


76 


77 


69.79 


32.54 


69.64 


32.85 


69.50 


33.15 


69 . 35 


33.45 


77 


78 


70.69 


32.96 


70 . 55 


33.27 


70.40 


33 . .58 


70.25 


33.89 


78 


79 


71.60 


33.39 


71.45 


33,70 


71.30 


34.01 


71.16 


34.32 


7S 


80 

81 


72.. 50 


33.81 


72.36 
73.26 


34.13 


72.21 


34.44 
34.87 


72.06 
72,96 


34,70 
35,19 


80 
81 


73.41 


34.23 


34.55 


73.11 


82 


74.32 


34,65 


74.17 


34.98 


74.01 


35.30 


73.80 


35.02 


82 


83 


75.22 


35.08 


75.07 


35.41 


74.91 


35.73 


74.76 


38.06 


83 


84 


76.13 


35.50 


75.97 


35.83 


75.82 


36.16 


75.66 


36,49 


84 


85 


77.04 


35.92 


76.88 


36.20 


76,72 


30,-59 


76.56 


36,93 


85 


86 


77.94 


36.35 


77,78 


36.08 


77,62 


37,02 


77.46 


37.30 


86 


87 


78.85 


36,77 


78.69 


37.11 


78,. 52 


37-45 


78.35 


37.80 


87 


88 


79.76 


37,19 


79.59 


37,54 


79.43 


37.88 


79.26 


38.23 


88 


89 


80.66 


37,61 


80.50 


37,96 


80.33 


38-32 


80.16 


38.07 


89 


90 
91 


81.57 


38,04 


81.40 


38.39 


81.23 


38.75 


81.06 


39.10 
39.53 


90 
91 


82.47 


38.46 


82.31 


38.82 


82.14 


39.18 


81.96 


92 


83.38 


38.88 


83.21 


39.24 


83.04 


39.01 


82.86 


39,97 


92 


93 


84.29 


39.30 


84.11 


39.67 


83,94 


40.04 


83.76 


40.40 


93 


94 


85.19 


39,73 


85.02 


40.10 


84.84 


40.47 


84.67 


40,84 


94 


95 


86.10 


40,15 


85.92 


40.52 


85.75 


40.90 


85,57 


41,27 


9^5 


96 


87.01 


40.57 


86.83 


40.95 


80.05 


41.. 33 


86,47 


41,71 


96 


97 


87.91 


40.99 


87.73 


41.38 


87.55 


41.70 


87,37 


42,14 


97 


98 


88.82 


41.42 


,88.64 


41.80 


88.45 


42.19 


88,27 


42.. 58 


98 


99 


89.72 


41.84 


89.54 


42.23 


89.36 


42,02 


89,17 


43,01 


99 


1^ 

i 

Q 


90.63 


42,26 


90.45 


42.66 


90,26 


43.05 


90,07 


43.44 


100 


Dep. 


Lat, 


Dep. 


La.. 


Dep, 


Lat. 


Dep. 


Lat. 


i 


65 Deg. 


641 Deg. 


64i Deg. 


64} Deg. 



54 



TRAVKRSE TABLE. 



1 

1 


26 Deg. 


264 Deg. 


26 h Deg. 


261 Deg. 1 



«■ 

3 




Lat. 


Dep. 


Lat. Dep. 


Lat. 1 Dep. 


Lat. 


Dep. 




r 


0.90 


44 


"O'.W 


0.44 


0.89 1 0.45 1 


0.89 


0.45 i 1 




2 


1.80 


0.83 


1.79 


0.88 


1.79 


0.89 


1.79 


90 2 




3 


2.70 


1.32, 


2.69 


1.33 


2.68 


1.34 


2.63 


1.35 3 




4 3.60 


1.75 


3.. 59 


1.77 


3.. 53 


1.78 


3.. 57 


I.80' 4 




5 4.49 


2.19 


4.48 


2.21 


4.47 


2.23 


4.46 


2 . 25 1 


5 




6 1 5.39 


2.63 


5.38 


2.65 


5.37 


2.68 


5.38 


2.70! 


6 




7 1 6.2!) 


3.07 


6.28 


3.10 


6.26 


3.12 


6.25 


3.15 


7 




81 7.19 


3.51 


7.17 


3.54; 


7.16 


3.57 


7.14 


3.60 


8 




9! 8.09 


3.95 


8.07 


3 . 93 ! 


8.05 


4.02 


8.04 


4.05 


9 




10 1 8.99 


4. 38 


8.97 


4.42 


8.95 4.46 


8.93 


4.. 50 


10 
11 




11 


9.89 


4.82 


9.87 


4.87 i 


9.84, 4.91 


9.82 


4.9.) 




12 


10.79 


5.26 


10.76 


5.3! 


10.74 5.35 


10.72 


5.40 


12 




13 


11.68 


5.70 


11.66 


5.75 


11.63! 5.80 


11.61 


5.85 


13 




14 


12.. 58 


6.14 


12.53 


6.19 


J 2. 53 


6.25 


12.. 50 


6.30 


14 




15 


13.4S 


6.58 


13.45 


6.63 


13.42 


6.69 


13.39 


6 . 75 


15 




16 


14.38 


7.01 


14.35 


7.08 


14.32 


7.14 


14.29 


7.20 


16 




17 


15.28 


7.45 


15.25 


7.. 52 


15.21 


7.59 


15.13 


7.65 


17 




18 


16.18 


7.89 


16.14 


7.96 


16.11 


8.03 


16.07 


8.10 


18 




19 


17.03 


8.33 


17.04 


8.40 


17.00 


8.48 


16.97 


8.. 55 


19 




20 
21 


17.98 


8.77 


17.94 


8.85 


17.90! 8.92 


17.86 
18.75 


9. GO 
9.45 


20 
21 




18.87 


9.21 


18.83 


9.29 


18.79 


9.37 




22 


19.77 


9.64 


19.73 


9.73 


19.09 


9.82 


19.65 


9.90 


22 




23 


20.67 


10.08 


20.63 


10.17 


20.. 58 


10.26 


20.. 54 


10.35 


23 




24 


21.. 57 


10.52 


21.52 


10.61 


21.48 


10.71 


21.43 


10.80 


21 




25 


22.47 


10.96 


22 . 42 


11.06 


22.37 


11.15 


22., 32 


11.25 


25 




26 


23.37 


11.40 


23 . 32 


11.50 


23.27 


11.00 


23.22 


11.70 


26 




27 


24.27 


11.84 


24.22 


11.94 


24.16 


12.05 


124.11 


12.15 


27 




28 


25.17 


12.27 


25.11 


12.38 


25.06 


12.49 


125.00 


12.60 


28 




29 


26.06 


12.71 


, 26.01 


12.83 


25 . 95 


12.94 


125.90 


13.05 


29 




30 


26.96 


13.15 


26.91 


13.27 


26.85 


13.39 


! 26.79 


1 3.. 50 


30 




31 


27.86 13.59 


27.80 


13.71 


27.74 


13.83" 


127.68 


13.S5 


TT 




32 


28.76 14.03 


28.70 


14.15 


28.64 j 14.28 


28.. 58 


14.40 


32 




33 


29.66 14.47 


29.60 


14.60 


29.. 53 ! 14.72 


129.47 


14.85 


33 




34 1.30.56! 14.90 


30.49 


15.04 


30.43 i 15.17 


! 30.36 


15.30 


34 




35 131.46 1 15.34 


31.39 


15.48 


31.32 1 15.62 


31.25 


15.75 


35 




36 


32.36 15.78 


.32 . 29 


15.92 


32.22 16.06 


32.15 


16.20 


36 




37 


33.26 1 16.22 


.33.18 


16.36 


33.11 16.51 


33.04 


16.65 


37 




38 


34.15 i 16.66 


34.08 


16.81 


34.01 16.96 


33.93 


17.10 


33 




39 


35.05 17.10 


34.98 


17.25 


34.90 17.40 


34.83 


17.55 


39 




40 


35.95 j 17.53 


35.87 i 17.69 


35.80 ! 17.85 


.35.72 
36.61 


18.00 


40 




41 136.85, 17.97 


36.77 1 18.13 


36.69 1 18.29 


1 18.45 


41 




42 37.75 18.41 


37.67 18. .58 


37. .59 I 18.74 


37.51 


i 18.90 


42 




43 33.65 18.85 


38.57 19.02 


.38.48 ! 19.19 


38.40 


i 19.35 


43 




44 39.55 19.29 


39.46 19.46 


39.38 19.63 


39.29 


1 19.80 


44 




45 40.45 19.73 


40.36 • 19.90 


40.27 I 20.08 


40.18 


20.25 


45 




46 


41.34 20.17 


41.26 20.35 


41.17 1 20.53 


41.08 


20.70 


46 




47 


42.24 20.60 


42.15 20.79 


42.06' 20.97 


41.97 


121.15 


47 




48 


43.14:21.04 


43.05 21.23 


42.96 121.42 


42.86 


i 21.60 


48 




49 


44.04 21.48 


43.95 21.67 


43.85 


21.86 


43.76 


1 22 . 05 


49 




50 


4^ ,94 121.92 


44.84 


22.11 


44.75 


22.31 


44.65 


1 22.50 


50 




i 

5 


Dep. 1 Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


i 

.2 




64 Deg. 


631 


Deg. 


63i 


Deg. 


63t Deg. 





TRAVERSE TABLE. 



55 



~5\ 


26 Deg. 


26i Deg. 


26i Deg. 


263 


Deg. 


"51 


Lat. 1 Dep. 


Lat. 


Dep. 


Lat. Dep. 

45T64 ^776 


Lat. 


Dep. 
22796 


45.84 22.33! 


45.74 


"22.56 


46 .54 


52 


46.74 22.80! 


46.64 


23.00 


46.54:23.20 


46.43 1 23.41 


52 


53 


47.64 23.23 1 


47.53 


23.44 


1 47.43 1 23.65 


47. 33 23.83 


53 


54 


4S.53 23.67 


48.43 23.88 


48.33 24.09 


48 22 24.31 


54 


55 


49.43 1 24.11! 


49.33 24.33 


49.22 1 24. .54 


49.11 24.76 


55 


56 


50.33 24.. 55, 


50.23 1 24.77 


50. 12 


24.99 


50.01 


25.21 


56 


57 


51.23 24.99 


51.12 25.21 


51.01 


25 43 


50.90 


25.66 


57 


58 


.52.13 25.43 


.52.02 25.65 


51.91 


25 68 


51.79 


26.11 


58 


59 


53.03 125.86 


.52.92 26.09 


52.80 


26.33 


52.69 


26.-56 


59 


60 
~6T 


53.93 26.30 


53.81 i 26.54 


53.70 


26 77 


.53.. 58 


27.01 


60 


54.83 ; 26.74 


.54.71 1 26.98 


54.59 


27.22 


54.47 


27.46 


61 


62 


.55.73 ' 27.18 


55.61 : 27.42 


.55.49 


27.66 


55.36 


27.91 


62 


63 


56.63 27.62 


56.50 '. 27.86 


.56.33 


23.11 " 56.26 ' 23.36 


63 


64 


57.. 52 2S.06 


57.40 ! 28.31 


.57.28 1 23.56 ,, 57.15 : 23.81 


64 


65 


58.42 , 28.49 


.58.30 123.75 


.53.17 1 29.00 j' 58.04: 29.26 


65 


66 


59.32 i 28.93 


59.19 i 29.19 


59.07 


29.45 58.94; 29.71 


66 


67 


60.22 29.37 


60.09 i 29.63 


59.96 


29.90 1 59.83 • 30.16 


67 


68 


61.12 29.81 


60.99 30.03 


60.86 


30.34 j] 60.72 30.61 


63 


C9 


62.02,30.25 


61.88 30.52 


61.75 


30.79 61.62, CI. 03 ! 69 1 


70 
71 


62.92 30.69 


62.78 ! 30.96 


62.65 


31.23 |! 62.51 j 31.51 1 70 j 


63.81 i 31.12 


63.68 ; 31.40 


63.. 54 


31.68 


63.40 131.98 i 71 


72 


64.71 31. .56 


64.57,31.84 


64.44 


32.13 


64.29 33.41 73 1 


73 


65.61 : 32.00 


65.47 1 33.29 


65.-33 


32.57 


65.19 .32.86 


73 


74 


66.51 32,44 


66.37) 32.73 


66.23 


33.03 ; 66.08 , 33.31 
33.46 1 66.97: 33.76 


74 


75 


67.41 I 32.88 


67.27! 33.17 


67.12 


75 


76 


68.31 f 33.32 


68.16 1 33.61 


68.01 133.91 i! 67.87 34.21 


76 


77 


69.21 ; 33.75 


69.06 ; 34.06 


63.91134.36 


63.76 34.66 j 77 


78 


70.11 34.19' 


69.96 34.50 


69.80 1 34.80 


69.65 35.11 78 


79 


71.00 34.63 


70.85' .34.94 


70.70 


35.25 


70..55 135.56 79 


80 
81 


71.90 : 35.07 
72.80 : 35.51 


71.75] 35.38 


71.59 


35.70 


71. 44i 36.01 80 
73.33' 36.46 ! 81 


72.65 1 35.83 


72.49 


36.14 


82 


73 . 70 35 . 95 


73.54 1 36.27 


73.38 


36.. 59 


73.22 36.91 


82 


83 


74 . 60 36 . 38 


74.44! 36.71 


74.28 


37.03 


74.12 ! 37.36 


83 


84 


75 . 50 36.82 


75.34137.15 


75.17 


37.48 !j 75.01 1 37.81 


84 


85 


76.40 37.26 


76. '-43 .37.59 


76.07 


37.93 ■' 75.90' 38.26 


85 


86 


77.30 37.70 


77.13 .33.04 


76.96 


.38.37 11 76.80 1 .33.71 


86 


87 


78.20 38.14 


78.03 33.48 


77.86 


38.82 


77.69 ! 39.16 


87 


88 


79.09 38.. 58 


78.92 38.92 


78.75 


39.27 


78.,53: 39.61 


88 


89 


79.99 39.01 


79.82 1 39.36 


79.65 j 39.71 


79.48 40.06 


89 


90 
91 


80.89 39.45 


80.72 I 39.81 


80.54; 40.16 


80.37, 40.51 i 90 1 


81.79 39.89 


81.62 140.25 81.44:40.60 


81.26 40.96 : 91 


92 


82.69 40.33 


82.51 1 40.69 il 82.33 41.05 Ij 82.15 41.41 t 92 


93 83.59 40.77 


83.41 41.13! 83.23! 41.50 i: 83.05 4L.8G | 93 


94 84.49 41.21 


84. 31 J 41. 58 i! 84. 12 141.94 83.94 42.31 i 94 


95 85.39 41.65 


85.20 42.021 85.02:42.39 84.83 42.76: 95 


96 86.28 42.08 


86.10 42.46 !' 85.91 i 42.83 85.73 43.21 96 


97 87.18 42.. 52 


87.00 42.901:86.81 43.28 n 86.62 43.66 97 


93 88.08 42. 9S 


,87.89 43.341' 87.70 43.73 !! 87.51 44.11 93 


99 88.98,43.40 


88.79,43.79 188.60,44.17 188.40 44.56 99 


100 

i 


89.88 ; 43.84 


89.69] 44.23 ll 89.49 44.63 1 89.30 , 45.01 100 


Dep. I Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 1 Lat. | § | 


1 














3 






r 




1 


s 


64 Deg. 


631 Deg. 


1 63| Deg. 

1 


63iDeg. S j 



66 



TEAVEKSE TABLE. 



o 

p 
p 

§ 

1 


27 Deg. 


27i Deg. 


27| 


Deg, 


271 Deg. 


"~1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 
~0T89 


Dep. 


Lat 


Dep. 


0.89 


0.45 


0.89 


0.46 


0,46 


0.88 


0.47 


2 


1.78 


0.91 


1.78 


0.92 


1.77 


0,92 


1.77 


0.93 


2 


3 


2.67 


1.36 


2.67 


1.37 


2.66 


1,39 


2.65 


1.40 


3 


4 


3.. 56 


1.82 


3.. 56 


1.83 


3.. 55 


1,85 


3.54 


1.86 


4 


5 


4.45 


2.27 


4.45 


2.29 


4.44 


2,31 


4.42 


2.33 


6 


6 


5.35 


2.72 


6.33 


2.75 


6.32 


2.77 


5.31 


2.79 


6 


7 


6.24 


3.18 


6.22 


3.21 


6.2) 


3.23 


6.19 


3.26 


7 


8 


7,13 


3.63 


7.11 


3.66 


7.10 


3.69 


7.08 


3.72 


8 


9 


8.02 


4.09 


8.00 


4.12 


7.98 


4.16 


7.96 


4.19 


9 


10 
11 


8.91 
9.80 


4.54 


8.89 


4.58 


8.87 


4.62 


8.85 


4.66 
5.12 


10 
11 


4.99 


9.78 


5.04 


9.76 


5.08 


9.73 


12 


10.69 


5.45 


10.67 


5.49 


10.64 


6.. 54 


10.62 


5.. 59 


12 


13 


11. .58 


5.90 


11.56 


5.95 


11.53 


6.00 


11. .50 


6.05 


13 


14 


12.47 


6.36 


12.45 


6.41 


12.42 


6.46 


12.39 


6.52 


14 


15 


13.37 


6.81 


13.34 


6.87 


13.31 


6.93 


13.27 


6.98 


15 


16 


14.26 


7,26 


14.22 


7.33 


14.19 


7.39 


14.16 


7.45 


16 


17 


15.15 


7.72 


15.11 


7.78 


15.08 


7.85 


15.04 


7.92 


17 


18 


16.04 


8.17 


16.00 


8.24 


15.97 


8.31 


15.93 


8..3S 


18 


19 


16.93 


8.63 


16.89 


8.70 


16.85 


8.77 


16.81 


8.85 


19 


2^ 
21 


17.82 


9.08 
9.. 53 


17.78 


9.16 


17.74 


9.23 


17.70 


9.31 


20 
~21 


18.71 


18.67 


9.62 


18.63 


9.70 


18.58 


9.78 


22 


19.60 


9.99 


19.56 


10.07 


19.51 


10.16 


19.47 


10.24 


22 


23 


20.49 


10.44 


20.45 


10.53 


20 . 10 


10.62 


20.35 


10.71 


23 


'^4 


21.38 


10.90 


21. .34 


10.99 


21.29 


11.08 


21.24 


11.17 


24 


25 


22.28 


11.35 


22.23 


11.45 


22.18 


11.54 


22.12 


11.64 


25 


26 


23.17 


11.80 


23.11 


11.90 


23.06 


12.01 


23.01 


12.11 


20 


27 


24.06 


12.26 


24.00 


12.36 


23.95 


12.47 


23.89 


12.57 


27 


28 


24.95 


12.71 


24.89 


12.82 


24.84 


12.93 


24.78 


13.04 


28 


29 


25.84 


13.17 


25.78 


13.28 


25.72 


13.39 


25.66 


13.50 


29 


30 
31 


26.73 


13.62 


26.67 


13.74 

14.19 


26.61 


13.85 


26.55 


13.97 


30 
31 


27.62 


14.07 


27.56 


27.. 50 


14.31 


27.43 


14.43 


32 


28.51 


14.53 


28.45 


14.65 


28.38 


14.78 


28.32 


14.90 


32 


33 


29.40 


14.98 


29.34 


15.11 


29.27 


16.24 


29.20 


15.37 


33 


34 


30.29 


15.44 


30.23 


15.57 


30,16 


15.70 


,30.09 


15.83 


34 


35 


31.19 


15.89 


31.12 


16.03 


31.05 


16.16 


30.97 


16.30 


35 


36 


32.08 


16.34 


32.00 


16.48 


31.93 


16.62 


31.86 


16.76 


36 


37 


32.97 


16.80 


32.89 


16.94 


32.82 


17.08 


32.74 


17.23 


37 


38 


.33.86 


17.25 


33.78 


17.40 


33.71 


17.55 


.33.63 


17.69 


38 


39 


34.75 


17.71 


34.67 


17.80 


34.. 59 


18.01 


34.51 


18.16 


39 


40 
41 


35.64 


18.16 


35.. 56 


18.31 
18.77 


35.48 


18.47 


35.40 


18.62 


40 
41 


36.53 


18.61" 


36.45 


36.37 


18.93 


36.28 


19.09 


42 


37.42 


19.07 


37 34 


19.23 


37.25 


19.39 


37.17 


19.56 


42 


43 


38.31 


19.52 


.38.23 


19.69 


38.14 


19.86 


38.05 


20.02 


43 


44 


39.20 


19.98 


39.12 


20.15 


39.03 


20.32 


38.94 


20.49 


4-4 


45 


40.10 


20.43 


,40.01 


20.60 


39.92 


20.78 


39.82 


20 . 95 


45 


46 


10.99 


20.88 


i 40.89 


21.06 


40.80 


21.24 


40.71 


21.42 


46 


47 


41.88 


21.34 


:41.78 


21.52 


41.69 


21.70 


41.59 


21.88 


47 


48 


42.77 


21.79 


42.67 


21.98 


42,58 


22.16 


42.48 


22.35 


48 


49 


4.]. 66 


22.25 


; 43.56 


22.44 


43,46 


22.63 


43.36 


22.82 


49 


50 

§ 

s 

s 

.2 

a 


44.55 


22.70 


44.45 


22.89 


44,35 


23.09 


44.25 


23.28 


_50 

1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


63] 


:»eg. 


62| Deg. 


621 


Deg. 


62i 


Deg. 



TRAVERSE TABLE. 



£7 



a 

3 
? 

"51 


1 

27 Deg. 


21i Deg. 


.m 


Dog. 


271 Deg. 


c 

3 

"sT 


Lat. 


Dep. 


Lat. 1 Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


45.44 


23.15 


45.34 


23.35 


45.24 


23.55 


45.13 


23775" 


52 


46.33 


23.61 


46.23 


23,81 


46,12 


24.01 


46,02 


24.21 


52 


53 


47.22 24.06 


47.12 


24,27 


47,01 


24.47 


46,90 


24.68 


53 


54 


48.11 


24.52 


48.01 


24.73 


47,90 


24.93 


47.79 


25.14 


54 


55 


49.01 


24.97 


48.90 


25.18 


48.79 


25.40 


48.67 


25.61 


55 


56 


49.90 


25.42 


49.78 


25.64 


49; 67 


25.86 


49,56 


26.07 


56 


57 


50 . 79 


25.88 


50.67 


26.10 


50.56 


26.32 


.50.44 


26. .54 57 1 


58 


51.68 


26.33 


51.56 


26.56 


51.45 


26.78 


51.33 


27.01 


58 


59 


52.57 


26.79 


52.45 


27.01 


.52.33 


27.24 


52.21 


27.47 


59 


60 
61 


53.46 


27.24 


53.-34 


27.47 


.53.22 


27.70 


.53.10 


27.94 


60 
61 


54.35 


27.69 


54.23 


27.93 


54.11 


28.17 


53 . 98 


28.40 


62 


55.24 


28.15 


55.12 


28.39 


54.99 


23.63 


.54.87 


28.8? 


62 


63 


.56.13 


28.60 


.56.01 


28.85 


55.88 


29.09 


55.75 


29.33 


63 


64 


57.02 


29.06 


56.90 


29.30 


56,77 


29.55 


56,64 


29.80 


64 


65 


57 92 


29. M 


57.79 


29.76 


157,66 


30.01 


57.52 


30.26 


65 


66 


.58.81 


29 . 96 


.58.68 


30.22 


158.54 


30.48 


58.41 


30.73 


66 


67 


.59.70 


30.42 


59.50 


30.68 


59.43 


30.94 


59.29 


31.20 


67 


68 


60.59 


30.87 


60.45 


31.14 


60.32 


31.40 


60.18 


31.68 


68 


69 


61.48 


31.33 


61.34 


3J.59 


61.20 


31.86 


61.06 


32.13 


69 


70 
71 


62.37 


31.78 


62.23 


32.05 


62.09 


32.32 


61.95 


32.59 
33.06 


70 
71 


63.26 


32.23 


6?. 12 


32.51 


62.98 


32.78 


62.83 


72 


64.15 


32.69 


64.01 


32.97 


63.86 


.33.25 


63.72 


33.52 


72 


73 


65.04 


33.14 


64.90 


33.42 


64,75 


33.71 


64.60 


33 . 99 


73 


74 


65.93 


33 . 60 


65.79 


33.88 


65,64 


34.17 


65.49 


34.46 


74 


75 


66.83 


34.05 


66.68 


.34.34 


66.. 53 


34.63 


66.37 


34.92 


75 


76 


67.72 


34.50 


67.57 


34.80 


67.41 


35,09 


67.26 


.35.39 


76 


77 


68.61 


34.96 


68.45 


35.26 


68.30 


35.55 


68.14 


35.85 


77 


78 


69.50 


.35.41 


69.34 


35.71 


69.19 


36.02 69.03 


36.32 


78 


79 


70 . 39 


35.87 


70.23 


36.17 


70.07 


36.48 


69.91 


36.78 


79 


80 
81 


71.28 


36.32 


71. 12 
72.01 


36.63 


70.96 


36.94 


70,80 


37.25 


80 
81 


72.17 


36.77 


37.09 


71,85 


37.40 


71.68" 


37.71 


82 


73.06 


37.23 


72.90 


37.. 55 


72.73 


37.86 


72.. 57 


38.18 


82 


83 


73.95 


37.68 


73.79 


38.00 


73 . 62 


38.33 


73.45 


38.65 


83 


84 


74.84 


38.14 


74.68 


38.46 


74.51 


38,79 


74.34 


39.11 


84 


85 


75.74 


38.59 


75.57 


33.92 


75.40 


39.25 


75.22 


39.. 58 


85 


86 


76.63 


39.04 


76.46 


39.38 


76.28 


39.71 


76.11 


40.04 


86 


87 


77.52 


39.. 50 


77.34 


39.83 


77.17 


40.17 


76.99 


40.51 


87 


88 


78.41 


39.95 


78.23 


40.29 


78.05 


40.63 


77.88 


40.97 


88 


89 


79.30 


40.41 


79.12 


40.75 


78.94 


41.10 


78.76 


41.44 


89 


90 
91 


80.19 


40.86 


SO. 01 


41.21 


79.83 


41. .56 


79.65 


41.91 


90 
91 


81.08 


41.31 


80.90 


41.67 


80.72 


42.02 


80.53 


42.37 


92 


81 ,97 


41.77 


81.79 


42.12 


81.60 


42.48 


81.42 


42.84 


92 


93 


82.86 


42.22 


82.68 


42.58 


82,49 


42.94 


82.30 


43.30 


93 


94 


83.75 


42.68 


83.57 


43.04 


83.. 38 


43.40 


83.19 


43 . 77 


94 


95 


84.65 


43.13 


84.46 


43.50 


84.27 


43.87 


84.07 


44.23 


95 


96 


85.54 


43.. 58 


85.35 


43.96 


85.15 


44.33 


84.96 


44.70 


96 


97 


86.43 


44.04 


86.23 


44.41 


86.04 


44.79 


85.84 


45.16 


97 


98 


87.32 


44.49 


87,12 


44.87 


86.93 


45.25 


86.73 


45.63 


98 


99 


88.21 


44.95 


88.01 


45.33 


87,81 


45.71 


87.61 


46.10 


99 


100 


^9.10 
Dep. 


45.40 


88.90 


45.79 


88.70 


46,17 


88.50 


46.56 


100 

1 


Lat. 


Dep. 


Lat. 


Dep, 


Lat. 

1 


Dep. 


L.. 


63 Deg. 


621 Deg. 


62_l Deg. 


62i Deg. 



58 



TKAVERSE TABLE. 



1 


28 Deg. 


28i Deg. 


1 

28i Deg. 


281 Deg. 


a 

1 

1 


Lat. 


Dep. 


Lat. 

0.88 


Dep. 


Lat. 


Dep. 


LatT 


Dep. 

0.48 


1 


0.88 


0.47 


0.47 


0,88 


0.48 


0.88 


2 


1 . 77 


0.94 


1.76 


0.95 


1,76 


0.95 


1.75 


0.96 


2 


3 


2.65 


1.41 


2.64 


1.42 


2.64 


1.43 


1 2.63 


1.44 


3 


4 


3.. 53 


1.88 


3.52 


1.89 


3.. 52 


1.91 


3.. 51 


1.92 


4 


5 


4.41 


2.35 


4,40 


2.37 


4,39 


2.39 


4.38 


2.40 


5 


6 


5.30 


2.82 


5.29 


2.84 


5.27 


2,86 


5.26 


2.89 


6 


7 


6.18 


3.29 


6.17 


3.31 


6.15 


3.34 


6.14 


3.37 


7 


8 


7.06 


3.76 


7.05 


3.79 


7.03 


3.82 


7.01 


3.85 


8 


9 


7.95 


4.23 


7.93 


4,26 


7.91 


4.29 


7.89 


4.33 


9 


10 


8.83 


4.69 


8.81 


4.73 


8.79 


4.77 


8.77 


4.81 


10 


11 


9.71 


5.16 


9.69 


5.21 


9.67 


5.25 


9.64 


5.29 


11 


12 


10.60 


5,63 


10.57 


5,68 


10.55 


5.73 


10.52 


5.77 


12 


13 


11.48 


6,10 


11.45 


6.15 


11.42 


6.20 


11.40 


6.25 


13 


14 


12.36 


6,57 


12.33 


6.03 


12.30 


6.68 


12,27 


6.73 


14 


15 


13.24 


7.04 


13,21 


7.10 


13.18 


7.16 


13.15 


7.21 


15 


16 


14.13 


7.51 


14.09 


7.57 


14.06 


7.63 


14.03 


7.70 


16 


17 


15.01 


7.98 


14.98 


8.05 


14,94 


8,11 


14.90 


8.18 


17 


18 


15.89 


8.45 


15.86 


8.52 


15.82 


8,59 \' 15,78 


8.66 


18 


19 


16.78 


8.92 


16.74 


8.99 


16.70 


9,07 16,66 


9.14 


19 


20 
21 


17.66 

18.54 


9.39 
9.86 


17.62 
18.50 


9.47 
9.94 


17.58 


9,54 ' 17. .53 
10.02: 18.41 


9.62 


20 


18.46 


10.10 


21 


22 


19.42 


10.33 


19.. 38 


10.41 


19.33 


10.50 ; 19.29 


10.. 58 


22 


23 


20.31 


10.80 


20.26 


10.89 


20.21 


10.97 20.16 


11.06 


23 


24 


21.19 


11.27 


21.14 


11. .36 


21.09 


11,45 ,21,04 


11.. 54 


24 


25 


22.07 


11.74 


22.02 


11.83 


21.97 


11.93 


21.92 


12.02 


25 


26 


23.96 


12.21 


22 . 90 


12.31 


22.85 


12.41 


22 . 79 


12.51 


26 


27 


23.84 


12.68 


23.78 


12.78 


23.73 


12.88 


23.67 


12.99 


27 


28 


24.72 


13.15 


24.66 


13.25 


24.61 


13.36 


24.. 55 


13.47 


28 


29 


25.61 


13.61 


25.55 


13.73 


25.49 


13.84 


25.43 


13.95 


29 


30 
31 


26.49 
27.37 


14.08 
14.55 


26.43 


14.20 


26.36 
27.24 


14.31 
14,79 


26.30 
27.18 


14.43 
14.91 


30 
31 


! 27.31 


14.67 


32 


28.25 


15.02 


28.19 


15.15 


28.12 


15.27 


28.06 


15.30 


32 


33 


29.14 


15.49 


29.07 


15.62 


29.00 1 15.75 


28.93 


15.87 


33 


34 


30 . 02 


15.96 


29.95 


16.09 


29.88 


16.22 


29.81 


16.35 


34 


35 


30.90 


16.43 


30.83 


16.57 


30.76 


16.70 


30.69 


16 83 


35 


36 


31.79 


16.90 


31.71 


17.04 


31.64 


17,18 


31.56 


17.32 


36 


37 


32.67 


17.37 


32.59 


17.51 


32 . ^^2 


17.65 


32.44 


17.80 


37 


38 


33.55 


17.84 


133.47 


17.99 


33.39 


18.13 


.33.. 32 


18.28 


38 


39 


34.43 


18.31 


1,34.35 


18.46 


34.27 


18.61 


34.19 


18.76 


39 


40 
41 


35.32 
36.20 


18.78 
19.25 


i 35.24 


18.93 
19, 4f 


35.15 
36". 0« 


19,09 
19,. 5 6 


35,07 
35.95 


19.24 
19.72 


40 
41 


36.12 


42 


37.08 


19.72 


37.00 


19.88 


36.91 


20 . 04 


36.82 


20.20 


42 


43 


37.97 


20.19 


37.88 


20.35 


37.79 


20,52 


37.70 


20,68 


43 


44 


38. S5 


20.66 


38.76 


20.83 


38 . 67 


20.99 


38.. 58 


21.16 


44 


45 


39.7-3 21.13 


39.64 1 21. .30 


39.. 55 


21.47 


3 J. 45 


21.64 


45 


46 40.62 21.60 


40.52 


21.77 


40.43 


21.95 


40.33 


22.13 


46 


47 4I..50I 22.07 


41.40 


22.25 


41.30 


22.43 


4i.21 


22-61 


47 


48 42.38 ; 22.53 


42.28 


22.72 


42.18 


22.90 


42.08 


23.09 


48 


49 43.26 123.00 


43.16 


23.19 


43,06 


23.. 38 


42.96 


23.57 


49 


50 


44.15'! 23.47 


44.04 


23.67 


43,94 


23.86 


43.84 


24.05 


_50 


i 

5 


Dep. 1 Lat. 


Dep. 


Lat. 


Dep, 


Lat. 


Dep. 


Lat 


5 

5 


62 Deg. 


61| Deg. 


ei^Deg. 


dH Deg. 



TRAVERSE TACtK. 





*^ 1 

28 Deg. 


m Deg. 


28iDeg. 1 


281 Deg. 


5 

§ 

'tl 


Lat. 1 Dep. ! 


Lat. 1 Dep. 


Lat. 


Dep. 


Lat. 


Dep.! 


45.03 1 23.94; 


44.93 124. 14 


44.82 1 24.34! 


44.71 


24.133 1 


52 


45.91 124.41 U5.81 1 24.C1 j 


45.70 24.811 


45.. 59 


25.01 


52 


53 


46.80 24.88 i 46.69 [25.09 


46.58 ' 25.29 1 


46.47 


25.49 


53 


54 47. 68! 25. 35 47. 57; 25. 56^1 47. 46 0577 


47.34 


25.97 


54 


55 48. . 56 ! 25.82 48.45 1 26.03 1; 48.33 26 .24 


48.22 


26.45 


5.^ 


.56 49.45 26.29 49.33 ! 26.51 '! 49.21 26.72; 


49.10 


26.94 


56 


.57 ,50.33 26.76 50.21 


26.98 1 


.50.09 27.20 1 


49.97 127.42 


57 


58 51.21 ' 27.23 51.09 


27.45 1 


50.97 


27.68 li 50.85 127.90 


58 


59 


52.09 27.70 51.97 


27.93 1 


51.85 


28,15 1, 51,73 28.38 


59 


60 


52. 9S 
"53.86 


28.17 ;. 52. 85 


28.40 i 


,52.73 


28.63!: 52.60 ! 28,86 


60 

-6T 


28.64 .53.73 


28.87! 


53.61 


20.11 1 53.48 


29.34 




54.74 29.11 54.62 


29.35 154.49 


29.58 


54.36 


29.82 


62 


63 


55.63 i 29.58 55.i=i0 1 29.82 i .55.37 


30.06 i 


55.23 


30.30 


63 


64 


56.51 130.05': 56.38 


30.29 


56.24 


30., 54 


56.11 


30.78 


64 


65 


57.39 1 30.52 157.26 


30.77 


57.12 


31.02 


50.99 


31.26 


65 


66 


.58.27 i 30.99 i .58.14 


31,24 


.58.00 


31.49 


.57.86 


31.75 


66 


07 


59.16 31.45 ■ 59.02 


31.71 


58.88 


31.97 


58.74 


32.23 


67 


68 


60.04 31.92 59.90 


.32.19 


69.76 


32.45 


59.62 


32.71 


68 


69 


60.92 ; 32.39 160.78 


32 . 60 


60 . 64 


32.92 


60.49 


33.19 


69 


70 


61.81 132.86 


61.60 


.33.13 


61.52 


33.40 
33.88 


61.37 


33.67 
34.15 


70 

71 


71 ;62T69 ; 33..33 


62.54 


33.61 


62.40 


62.25 


72 63.57 i 33.80 


63.42 


34.08 


63.27 


.34.36 


63.12 


34.63 


72 


73 


64.46 1 .^.27 


64.30 


34.55 


64.15 


34.83 


64.00 


35.11 


73 


74 


65.34 34.74 ;| 65.19 


35.03 


65.03 


35.31 


64.88 


35.59 


74 


75 


66.22 i 35.21 i; 66.07 


35.. 50 


65.91 1 35.79 


05.75 


36.07 


75 


76 


67.10 35.68 1 66.95 


35.97 


66.79 136.26 


66.63 


36.50 


70 


77 


67.99! 36.15:1 67.83 


30.45 


67.67 136.74 


67.51 


37.04 


77 


78 


63.87 36.62 68.71 


36.92 


68..55 137.22 


68.38 


37.. 52 


78 


79 


69.75 37.09,1 69.59 


37.39 


69.43 37.70 


69.26 


38.00 


79 


80 
81 


70.64 37.. 56 


70.47 


37.87 


70,31 138,17 


1 70.14 


38.48 


80 
81 


71.52 38.03 


71.35 


38.34 


71.18 


33 . 65 


: 71.01 


38.96 


82 


72.40 : 38.. 50 


72.23 


38.81 


72.06 


39.13 


171.89 


39.44 


82 


S3 


73.28 1 38.97 


73.11 


39.29 


72.94 


39,60 


72.77 


39.92 


88 


84 


74.17 ' 39.44 


73.99 


39.70 


73.82 


40.08 


173.64 


40.40 


84 


85 


75.05 I 39.91 


74.88 


40.23 


74.70 


40,. 56 


74.52 


40.88 


85 


86 


75.93 40.37 


75.76 


40.71 


75 58 


41.04 


75.40 41.36 


86 


87 


76.82:40.84 


76.64 


41.18 


76.46 


41.51 


76.28 41.85 


87 


88 


77.70 i 41.31 


77.52 


41.65 


77.34 


41.99 


!77.15 I42..33 


88 


89 


78.58 141.78 


78.40 


42.13 


178.21 


42.47 


,78.03 142.81 


89 


90 
91 


79.47 142.25 


79.28 


42.00 


79.09 


42.94 


1 78.91 ! 43.29 

79.78:43.77 


90 
91 


80.35 


42.72 


80.16 


43.07 


79.97 


43.42 


92 


81.23 


43.19 


81.04 


43.55 


80.85 


43.90 


180.66 ! 44.25 


92 


93 


82.11 


43.66 


81.92 


44.02 


81.73 44.38 


' 81.54 '44.73 


93 


94 


83.00 


44.13 


82.80 


44.49 


82.61 i 44.85 


82.41 45.21 


94 


95 


83.88 


44.60 i! 83.68 


44.97 


83.49 45.33 


83.29 45.69 


95 


96 


S4.76 145.07!! 84.57 


145.44 1184.37 45.81 


'84.17 46.17 


96 


97 


85.65 45..54I 85.45 


45.91 85.25 1 46.28 


85.04 46.66 


97 


98 


86. .53 46.01 i! 86.33 j 46.39 || 86. 12 146.76 


185.92 47.14 


98 


99 


87.41 46.48 :| 87.21 , 46.86 i! 87.00 | 47.24 


; 86.80 47.62 


99 


J 00 


83.29 46.95 1; 88.09 47.33 ;; 87.88 . 47.72 


1 87.67 ,48.10 
Dep. ! Lat. 


100 

1 

1 <^ 


5 


Dep. j Lat. 


Dep. : Lat. 


Dep. ! Lat. 


62 Deg. 


1 

1 61| Deg. 


eii Deg. 


6U Deg, 



TRAVERSE TABLE. 



1 

CD 


29 Deg. 

1 


294 Deg. 


29i Deg. 


291 Deg. 


s 

1 


Lat. 
-0787 


Dep. 


Lat. 


Dep. 


Lat. Dep. 


Lat. 


Dep. 


0.48 


0.87 


0.49 


0.87 0.49 1 


0,87 


0.,50 


2 


1.75 


0.97 


1.74 


0.98 


1.74 0.98 1 


1,74 


0.99 




3 


2.62 


1.45 


2.62 


1.47 


2.61 1 


1,48 


2,60 


1.49 


3 


4 


3.. 50 


1.94 


3.49 


1.95 


3.48 


1,97 


3,47 


1,98 


4 


5 


4.37 


2.42 


4.36 


2.44 


4.35 


2,46 


4,34 


2,48 


5 


6 


5.25 


2.91 1 


5,23 


2.93 


5.22 


2.95 


5.21 


2,98 


6 


7 


6.12 


3.391 


6.11 


3.42 


6.09 


3,45 


6,08 


3,47 


7 


8 


7.00 


3.88 j 


6.98 


3.91 


6.96 


3.94 


6.95 


3.97 


8 


9 


7.87 


4.36 1 


7.85 


4.40 


7.83 


4.43 


7,81 


4.47 


9 


10 
if 


8.75 
9'.02 


4.85 1 
5.33 1 


8 . 72 
9.00 


4.89 


8.70 


4,92 
6.42 


8,68 


4.90 


10 


5.37 


9.. 57 


9,55 


5.46 


11 


12 


10.50 


5.82 


10.47 


5.86 


10.44 


5.91 


10,42 


5.95 


12 


13 


11.37 


6.30 1 


1 1 . 34 


6.35 


11.31 


6.40 


11,29 


6.45 13 


14 


12.24 


6.79 


12.21 


6.84 


12.18 


6.89 


12.15 


6.95 14 


15 


13.12 


7.27 


13.09 


7.33 


13.06 


7.39 


13.02 


7.44 : 15 


16 


13.99 


7.76 


13.96 


7.82 


13.93 


7.88 


13.89 


7,94; 16 


17 


14.87 


8.24 


14.83 


8.31 


14. SO' 


R.37 


14.76 


8,44 1 17 


IS 


15.74 


8.73 


15.70 


8.80 


15.67 


8.86 


15,63 


8.93 


18 


19 


16.62 


9.21 


16.58 


9.28 


16.54 


9.36 


16.50 


9.43 


19 


20 

21 


17.49 
18.37" 


9.70 
10. LS' 


17.45 
"is. 32 


9.77 
10.26 


17.41 
18.28' 


9.85 
10.34 


17.36 


9.92 


20 


18.23 


10.42 


21 


22 


19.24 


10.67 i 19 19 


10.75 


19.15 


10.83 


19.10 


10.92 


22 


23 


20.12 


11.15 : 20.07 


11.24 


20.02 


11.33 


19.97 


11.41 


23 


24 


20.99 


11.64 


20.94 


11.73 


20.89 


11.82 


20.84 


11.91 


24 


25 


21.87 


12.12 


21.81 


12.22 


21.76 


12.31 


21.70 


12.41 


25 


26 


22 . 74 


12.60 


22.68 


12.70 


22.63 


12.80 


22.57 


12.90 


26 


27 


23.61 


13.09 


23 . 56 


13.19 


23.50 


13,30 


23.44 


13.40 


27 


28 


24.49 


13.57 


24.43 


13.68 


24.37 


13.79 


24.31 


13.89 


28 


29 


25.. 36 


14.06 


25.30 


14.17 


25.24 


14.28 


25.18 


14.39 


29 


30 


26.24 


14.. 54 


20.17 


14.06 


26.11 


14.77 


26.05 


14.89 I 30! 


"31 


27.11 


15.03 


27.05 


1,5.15 


26.98 


15.27 


26.91 


15.38 


31 


32 


27.99 


15.51 


27.92 


15.64 


27.85 


15.76 


27.78 


15. 8M 


32 


33 


28.86 


16.00 


28.79 


16.12 


28.72 


16.25 


28 . 65 


16.38 


33 


34 


29 . 74 


16.48 


29 . 66 


16.61 


29.59 


16. r4 


29 . 52 


16.87 


34 


35 


30.01 


16.97 


30 . 54 


17,10 


30.46 


17.23 


.30.39 


17.37 


35 


36 


31.49 


17.45 


31.41 


17.59 


31.33 


17.73 


31.26 


17.86 , 36 I 


37 


32.36 


17.94 


32 . 28 


18.08 


32.20 


18.22 


32.12 


18.36 


37 


38 


33.24 


18.42 


33.15 


18.. 57 


33 . 07 


18.71 


32.99 


18.86 


38 


39 


34.11 


18.91 


34.03 


19.00 


33.94 


19.20 


33.86 


19.35 


39 


40 
41 


.34.98 
.35 . 86 


19.39 
19.88 


34.90 
3"5 . 77 


19.. 54 
20.03 


34.81 


19.70 


34.73 


19.85 


40 

41 


35.68 1 20.19 


35.60 


20.34 


42 


36.73 


20 . 36 


36 . 64 


20.. 52 


36.55:20.68 


36.46 


20.84 


42 


43 


37.61 


20.85 


37., 52 


21.01 


37.43 121.17 


37.33 


21.34 


43 


44 


.38.48 


21.33 


38.39 


21.50 


38.30 


21.67 


38.20 


21.83 


44 


45 


.39.36 


21.82 


39.26 


21.99 


39.17 


22.16 


39.07 


22.. 33 


45 


46 140.23 


22.30 


40.13 


22.48 


1 40.04 


22.65 


39.94 


22.83 


j 46 


47 1 4 1 . 1 1 


22 . 79 


41.01 


22.97 


40.91 


23.14 


40.81 


23.32 


1 47 


48 41.98 


23.27 


1 41.88 


23.45 


41.78 


23 . 68 


41,67 


23.82 


48 


49! 42.86 


23.70 


1 42.75 


23.94 


42,65 


24.13 


42,54 


24.31 


49 


50 1 43.73 


24 '.24 


43.62 


24.43 


43.. 52 


24.62 


43.41 


24,81 


50 

1 1 


i 


Dep. j Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dop. 


Lat, 


.2 


61 Deg. 

1 


601 


Deg. 


60J Deg. 


60i Deg. 



TRAVERSE TABLE. 



61 



r _ 


29 Deg. 


29i Deg. 


29^ Deg, 


291 Deg. 


1 


1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat, 


Dep. 


Lat. 


Dep, 


IT 


44.61 


24.73 


44.50 


24.92 


44,39 


25.11 


44.28 


25T3T 


~51 


52 


45.48 


25.21 


45.37 


25.41 


45.26 


25.61 


45.15 


25,80 


52 


63 


46.35 


25.69 


46,24 


25.90 


46.13 


26.10 


46.01 


26 . 30 


53 


54 . 


47.23 


26.18 1 


47.11 


26.39 


47.00 


26.59 


46.88 


26,80 


5.) 


55 1 


48.10 


26. G6 


47.99 


26.87 


47.87 


27.08 


47,75 


27,29 


55 


5fl 


48.98 


27.15 


48.86 


27.36 


48.74 


27.. 58 


48.62 


27,79 


56 


57 


49.85 


27.63 


49.73 


27.85 


49.61 


28.07 


49.49 


28. 2S 


57 


5S 


50 . 73 


28.12 


50.60 


28 . 34 


50.48 


28.56 


50.36 


23.78 


58 


59 


51.60 


28.60 


51.48 


28.83 


51.35 


29.05 


51.22 


29. 2S 


59 


60 
fil 


.52.48- 
53.35 


29.09 
29.57 


52.35 


29.32 


52.22 


29.55 
30.04 


52.09 
52.96 


29.77 


60 
61 


.53.ii2 


29.81 


.53.09 


30 . 27 


62 


54.23 


30.06 


54.09 


30.29 


53.96 


30.. 53 


53.83 


30.77 


62 


63 


55.10 


30.54 1 


54.97 


30.78 


54.83 


31.02 


54.70 


31.26 


63 


G4 


55.98 


31.03 


55.84 


31.27 


55.70 


31.52 


55.56 


31.76 


64 


65 


56.85 


31.51 ! 


56.71 


31.76 


56.57 


32.01 


56.43 


32.25 


65 


00 


57.72] 32.00 1 


57.. 58 


32.25 


57,44 


32.50 


.57.30 


32.75 


06 


67 


.58.60 1 32.48 j 


.58.46 


32.74 


.58.31 


32.99 


58.17 


33.25 


67 


68 


.59.17! 32.97 


59.33 


33.23 


59.18 


33.48 


59.04 


33.74 


68 


69 


60.35 


33.45' 


60.20 


33.71 


60.05 


33.98 


,59.91 


34.24 


69 


70 

TI 


61.22 


33.94, 

34.42 ; 


61.07 


34.20 


60.92 


,34.47 


60.77 
61.64 


34,74 


70 

71 


62.10 


61.95 


.34.69 


61.80 


34.96 


35.23 


72 


62.97 


34.91 


62.82 


35.18 


62.67 


35,45 


62.51 


35.73 


72 


73 


63.85 


35.39 


63.69 


35.67 


63.54 


35.95 


63.38 


36.22 


73 


74 


64.72 


35.88 


64.56 


36.16 


64.41 


36.44 


64.25 


36.72 


74 


75 


65.60 


36.36 


65.44 


36.65 


65.28 


36.93 


65.11 


37.22 


75 


76 


66.47 


36.85 


66.31 


37.14 


66.15 


37.42 


65.98 


37.71 


76 


77 


67.35 


37.33 


07.18 


37.62 


67.02 


37,92 


66.85 


38.21 


77 


7S 


68.22' 37.82 


68.05 


38.11 


67.89 


38,41 


67.72 


38.70 


78 


79 


69.09 


38.30 


68.93 


38.60 


68.76 


38.90 


68.59 


39.20 


79 


80 
81 


69.97 
70.84 


38.78 


69.80 


39.09 
39.58 


69.63 


39.39 


69.46 


39.70 


80 


39.27 


70.67 


70.. 50 


39.89 


70.32 


40.19 


82 


71.72 


39.75 


71.54 


40.07 


71.37 


40.38 


71.19 


40,69 


82 


83 


72 . 59 


40.24 


72.42 


40.56 


72.24 


40.87 


72.06 


41,19 


83 


84 


73.47 


40.72 


73.29 


41.04 


73.11 


41,36 


72.93 


41.68 


84 


85 


74.34 


41.21 


74.16 


41.53 


73.98 


41,86 


73.80 


42.18 


85 


86 


75.22 


41.69 


75.03 


42,02 


74.85 


42.35 


74.67 


42.67 


86 


87 


76 . 09 


42.18 


75.91 


42.51 


75.72 


42.84 


75 . 53 


43.17 


1 87 


88 


76.97 


42.63 


76.78 


43.00 


76.59 


43.33 


76.40 


43.67 1 88 


89 


77.84 


43.15 


77.65 


43.49 


77.46 


43.83 


77.27 


44.16 1 89 


90 
91 


78.72 


43.63 


78.52 
79.40 


43.98 


78.33 
79.20 


44.32 
44.81 


78.14 


M.66 


90 
91 


79.-59 


44.12 


44.46 


79.01 


45.16 


92 


80.46 


44.60 


80.27 


44.95 


80.07 


45.30 


79.87 


45,65 i 92 


93 


81.34 


45.09 


81.14 


45,44 


80.94 


45 . 80 


80,74 


46.15 


93 


94 


82.21 


45 . 57 


82.01 


45.93 


81.81 


46.29 


81,61 


46.64 


94 


95 


83.09 46.06 


82.89 


46.42 


82.68 


46.78 


82.48 


47.14 


95 


96 


83.96 46.. 54 


83.76 


46.91 


83.55 


47.27 


83.35 


47.64 


96 


97 


: 84.84 47.03 


84.63 


47.40 


84.42 


47.77 


84.22 


48.13 


97 


■98 


185.71 1 47.51 


85.50 


47.88 


85.29 148.26 


85,08 


48.63 


98 


99 


86.59 48.00 


86.38 


48.37 


86.17 


48.75 


85,95 


49.13 


99 


100 

1 
.2 

Q 


'87.46 148.48 


87.25 


48,86 
Lat, 


87.04 


149.24 


86,82 


49.62 


100 


Dep. 1 Lat. 


Dep. 


Dep. 


Lat, 


Dep. 


Lat, 


i" 


61 Deg. 


601 Deg. 


60^ Deg. 


60i Deg, 


.2 
Q 



23 



62 



TIIAVERSE TABLE. 





30 Deg. 


30i Deg. 


30^ Deg. 


301 Deg. 


f 
1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.87 


0..50 


0.86 


0.50 


0.86 


0.51 


0.86 


0.51 


2 


1.73 


1.00 


1.73 


1.01 


1.72 


1.02 1 


1.72 


1.02 


2 


3 


2.60 


1.50 


2.59 


1.51 


2.58 


1.52 1 


2.58 


1.53 


3 


4 


3.46 


2.00 


3.46 


2.02 


3.45 


2.03 


3.44 


2.05 


4 


5 


4.33 


2.50 


4.32 


2.52 


4.31 


2.54 


4.30 


2.56 


5 


6 


5.20 


3.00 


5.18 


3.02 


5.17 


3.05 


5.16 


3.07 


6 


7 


6.06 


3.50 


6.05 


3.53 


6.03 


3.55 


6.02 


3.58 


7 


a 


6.93 


4.00 


6.91 


4.03 


6.89 


4.06 


6.88 


4.09 


8 


9 


7.79 


4.50 


7.77 


4.53 


7.75 


4.57 


7.73 


4.60 


9 


10 
11 


8.66 


5.00 


8.64 


5.04 


8.62 


5.08 


8.59 


5.11 


10 
M 


9.53 


5.50 


9.. 50 


5.54 


9.48 


5.58 


9.45 


5.62 


12 


10.39 


6.00 


10.37 


6.05 


10.34 


6.09 


10.31 


6.14 


12 


13 


11.26 


6.50 


11.23 


6.55 


11.20 


6.60 j 


11.17 


6.65 


13 


14 


12.12 


7.00 


12.09 


7.05 


12.06 


7.11 


12.03 


7.16 


14 


15 


12.99 


7.50 


12.96 


7.56 


12.92 


7.61 


12.89 


7.67 


15 


16 


13.86 


8.00 


13.82 


8.06 


13.79 


8.12 


13.75 


8.18 


16 


17 


14.72 


8.50 


14.69 


8.56 


14.65 


8.63 


14.61. 


8.69 


17 


18 


15.59 


9.00 


15.55 


9.07 


15.51 


9.14 


15.47 


9.20 


18 


19 


16.45 


9.50 


16.41 


9.57 


16.37 


9.64 


10.33 


9.71 


19 


20 
21 


17.32 


10.00 


17.28 


10.08 


17.23 

18.09 


10.15 
10.66 


17.19 


10.23 


20 
21 


18.19 


10.50 


18.14 


10.58 


18.05 


10.74 


22 


19.05 


11.00 


19.00 


11.08 


18.96 


11.17 


18.91 


11.25 


22 


23 


19.92 


11.50 


19.87 


11.59 


19.82 


11.67 


19.77 


11.76 


23 


24 


20.78 


12.00 


20.73 


12.09 


20.68 


12.18 


20.63 


12.27 


24 


25 


21.65 


12.50 


21.60 


12.59 


21.54 


12.69 


21.49 


12.78 


25 


26 


22.52 


13.00 


22.46 


13.10 


22.40 


13.20 


22.34 


13.29 


26 


27 


23.38 


13.50 


23.32 


13.60 


23.26 


13.70 


23.20 


13.80 


27 


28 


24.25 


14.00 


24.19 


14.11 


24.13 


14.21 


24.06 


14.32 


28 


29 


25.11 


14.50 


25.05 


14.61 


24.99 


14.72 


24.92 


14.83 


29 


30 
31 


25.98 


15.00 


25.92 


15.11 


25.85 


15.23 


25.78 


15.34 


30 
31 


26.85 


15.50 


26.78 


15.62 


26.71 


15.73 


26.64 


15.85 


32 


27.71 


16.00 


27.64 


16.12 


27.57 


16.24 


27.. 50 


16.36 


32 


33 


28.. 58 


16.50 


28.51 


16.62 


28.43 


16.75 


28.36 


16.87 


33 


34 


29.44 


17.00 


29.37 


17.13 


29.30 


17.26 


29.22 


17.38 


34 


35 


30.31 


17.50 


30.23 


17.63 


30.16 


17.76 


30.08 


17.90 


35 


36 


31.18 


18.00 


31.10 


18.14 


31.02 


18.27 


30.94 


18.41 


36 


37 


32.04 


18.50 


31.96 


18.64 


31.88 


18.78 


31.80 


18.92 


37 


38 


32.91 


19.00 


32.83 


19.14 


.32.74 


19.29 


.32.66 


19.43 


38 


39 


33.77 


19.50 


33.69 


19.65 


33.60 


19.79 


33.52 


19.94 


39 


40 
IT 


34.64 


20.00 


34.55 


20.15 


34.47 


20.30 


34.38 


20.45 


40 
41 


35.51 


20.50 


35.42 


20.65 


35.33 


20.81 


.35.24 


20.96 


42 


36.37 


21.00 


36.28 


21.16 


36.19 


21.32 


36.10 


21.47 


42 


43 


37.24 


21. .50 


37.14 


21.66 


37.05 


21.82 


36.95 


21.99 


43 


44 


38.11 


22.00 


.38.01 


22.17 


37.91 


22.33 


37.81 


22.. 50 


44 


45 


38.97 


22.50 


38.87 


22.67 


.38.77 


22.84 


38.67 


23.01 


45 


46 


39.84 


23.00 


39.74 


23.17 


39.63 


23., 35 


39.. 53 


23.52 


46 


47 


40.70 


23.50 


40.60 


23.68 


40.50 


23.85 


40.39 


24.03 


47 


48 


41.57 


24.00 


41.46 


24.18 


41.36 


24.36 


41.25 


24.. 54 


48 


49 


42.44 


24.50 


42.33 


24.68 


42.22 


24.87 


42.11 


25.05 


49 


50 


43.30 


25.00 


43.19 


25.19 


43.08 


25.38 


42.97 


25.56 


50 

a 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


60 1 


yog. 


691 Deg. 


59\ 


Deg. 


59J Deg. 



TRAVERSE TABLE. 



63 



■ 1 


30 Deg. 


30i Deg. 


30i Deg. 


30 J Deg. 


O 

a 
P 
51 


Lat. 


Dep. 


Lat. 


D'ep. 


Lat. 


Dep. 


Lat. 


Dep. 


44.17 


25.50 


44.06 


25.69 


43.94 


25.88 


43.83 


26.08 


52 


45.03 


26.00 


44.92 


26.20 


44.80 


26.39 


44.69 


26.59 


52 


53 


45.90 


26.50 


45.78 


26.70 


45.67 


26.90 


'45.55 


27.10 


53 


54 


46.77 


27.00 


46.65 


27.20 


46.53 


27.41 


46.41 


27.61 


54 


55 


47.63 


27.50 


47.51 


27.71 


47.39 


27.91 


47.27 


28.12 


55 


56 


48.50 


28.00 


48.37 


28.21 


48.2r> 


28.42 


48.13 


28.63 


56 


57 


49.36 


28.50 


49.24 


28.72 


l49.ll 


28.93 


48.99 


29.14 


57 


58 


50.23 


29.00 


50.10 


29.22 


1 49.97 


29.44 


49.85 


29.65 


58 


59 


51.10 


29.50 


50.97 


29.72 


50.84 


29.94 


50.70 


30.17 


59 


60 
61 


51.96 


3U.00 


51.83 


30.23 


51.70 


30.45 


51.56 


30.68 


60 

61 


52.83 


30.50 


52.69 


30.73 


.52.-56 


30.96 


52.42 


31.19 


62 


53.69 


31.00 


53.56 


31.23 


53.42 


31.47 


53.28 


31.70 


62 


63 


54.56 


31.50 


54.42 


31.74 


54.28 


31.97 


54.14 


32.21 


63 


64 


55.43 


32.00 


55.29 


32.24 


55.14 


32.48 


55.00 


32.72 


04 


65 


56.29 


32.50 


56.15 


32.75 


56.01 


32.99 


55.86 


33.23 


65 


66 


57.16 


33.00 


57.01 


33.25 


.56.87 


33.50 


56.72 33.75 


66 


67 


58.02 


33.50 


57.88 


33.75 


.^7.73 


34.01 


57.58 


34.26 


67 


68 


58.89 


34.00 


58.74 


34.26 


58.59 


34.51 


.58.44 


34.77 


68 


69 


59.76 


34.50 


59.60 


34.76 


59.45 


35.02 


59.30 


35.28 


69 


70 
71 


60.62 


35.00 


60.47 


35.26 


60.31 


35.53 


60.16 


35.79 


70 


61.49 


35.. 50 


61.33 


35.77 


61.18 


36.04 


61.02 


36.30 


TI 


72 


62.35 


36.00 


62.20 


36.27 


62.04 


36.54 


61.88 


36.81 72 


73 


63.22 


36.50 


63.06 


36.78 


62.90 


37.05 


62.74 


37.32 73 


74 


64.09 


37.00 


63.92 


37.28 


63.76 


37.. 56 


63.60 


37.84 74 


75 


64.95 


37.50 


64.79 


37.78 


64.62 


38.07 


64.46 


38.35 75 


76 


65.82 


38.00 


65.65 


38.29 


65.48 


38.57 


65.31 


38.86 ! 76 1 


77 


66.68 


38.50 


66.52 


38 . 79 


66.35 


39.08 


G6.17 


39.37 


77 


78 


67.55 


39.00 


67.38 


39.29 


67.21 


39.59 


67.03 


39.88 


78 


79 


68.42 


39.50 


68.24 


39.80 


68.07 


40.10 


67.89 


40.39 


79 


80 
81 


69.28 


40.00 


69.11 


40.30 


68.93 


40.60 


68.75 


40.90 


80 


70.15 


40.50 


69.97 


40.81 


69.79 


41.11 


69.61 


41.41 


81 


82 


71.01 


41.00 


70.83 


41.31 


70.65 


41.62 


70.47 


41.93 


82 


83 


71.88 


41.. 50 


71.70 


41.81 


71.. 52 


42.13 


71.33 


42.44 


83 


84 


72.75 


42.00 


72.56 


42.. 32 


72.38 


42.63 


72.19 


42.95 


84 


85 


73.61 


42.50 


73.43 


42.82 


73.24 


43.14 


73.05 


43.46 


85 


86 


74.48 


43.00 


74.29 


43.32 


74.10 


43.65 


73.91 


43.97 


86 


87 


75.34 


43.50 


75.15 


43.83 


74.96 


44.16 


74.77 


44.48 


87 


88 


76.21 


44.00 


76.02 


44.33 


75.82 


44.66 


75.63 


44.99 


88 


89 


77.08 


44.50 


76.88 


44.84 


76.08 


45.17 


76.49 


45.51 


89 


90 
91 


77.94 


45.00 


77.75 


45.34 


77.55 


45.68 


77.35 


46.02 


90 


78.81 


45.50 


78.61 


45.84 


78.41 


46.19 


78.21 


46.53 


91 


92 


79.67 


46.00 


79.47 


46.35 


79.27 


46.69 


79.07 


47.04 


92 


93 


80.54 


46.50 


80.34 


46.85 180.13 47.20 


79.92 


47.55 


93 


94 


81.41 


47.00 


81.20 


47.35 180.99 147.71 


80.78 


48.06 


94 


95 


82.27 


47.50 


82.06 


47.86 i; 81.85 


48.22 


81.64 


48.57 


95 


96 


83.14 


48.00 


82.93 


48.36 .82.72 


48.72 


82.50 


49.08 


96 


97 


84.00 


48.50 


83.79 


48.87 ;l 83.58 


49.23 


83.36 


49.60 


97 


98 


84.87 


49.00 


84.66 


49.37 84.44 


49.74 


84.22 


50.11 


98 


99 


85.74 


49.60 


85.52 


49.87 85.30 


50.25 


85.08 


50.62 


99 


100 


86.60 


50.00 


86.38 


50.38 86.16 


50.75 


85.94 


51.13 


100 


1 

.2 


Dep. 


Lat. 


Dep. [ Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


c 


60 Deg. 


59i Deg. 


69i Deg. 


59i Deg. 



64 



TRAVERSE TABLE, 



2 

i 


31 Deg. 


3U Deg. 


3lh Deg. 

• 


31 1 Deg. 


O 

3 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.86 


0.51 


0.85 


~0T52" 


0.85 


0.52 


"oTss" 


0..53 


~T 


2 


1.71 


1.03 


1.71 


1.04 


1,71 


1.04 


1.70 


1.05 


2 


3 


2.57 


1.55 


2.56 


1.56 


2.56 


1.57 


2.55 


1..58 


3 


4 


3.43 


2.06 


3.42 


2.08 


3.41 


2.09 


3.40 


2. JO 


4 


5 


4.29 


2.58 


4.27 


2.59 


4.26 


2.61 


4.25 


2.63 


5 


6 


5.14 


3.09 


5.13 


3.11 


5.12 


3.13 


5.10 


3.16 


6 


7 


6.00 


3.61 


5.98 


3.63 


5.97 


3.06 


5.95 


3.68 


7 


8 


6.86 


4.12 


6.84 


4.15 


6.82 


4.18 


6.80 


4.21 


8 


9 


7.71 


4.64 


7.09 


4.67 


7.67 


4.70 


7.65 


4,74 


9 


10 
U 


8.57 
9.43 


5.15 


8.55 


5.ly 


8., 53 


5.22 


8.50 


5.26 


10 


5.67 


9.40 


5.71 


9.38 


5.75 


9.. 35 


5.79 


11 


12 


10.29 


6.18 


10.26 


6.23 


10.23 


6.27 


10.20 


6.31 


12 


13 


11.14 


6.70 


11.11 


6.74 


11.08 


6.79 


11.05 


6.84 


13 


14 13.00 


7.21 


11.97 


7.26 


11.94 


7.31 


11.90 


7.37 


14 


15 


12.56 


7.73 


12.82 


7.78 


12.79 


7.84 


12.76 


7.89 1 15 j 


16 


13.71 


8.24 


13.68 


8.30 


13.64 


8.36 


13.61 


8.42 16 1 


17 


14.57 


8.76 


14.53 


8.82 


14.49 


8.83 


14.46 


8.95 


17 


18 


15.43 


9.27 


15.39 


9.34 


15.35 


9.40 


15.31 


9.47 


IS 


19 


16.29 


9.79 


16.24 


9.86 


16.20 


9.93 


16.16 


10.00 


19 


20 


17.14 


10.30 


17.10 


10.. 38 


17.05 
17.91 


10.45 


17.01 


10,52 


20 


21 


18.00 


10.82 


17.95 


10.89 


10.97 


17.86 


11.05 


~2T 


22 


18.86 


11.33 


18.81 


11.41 


18.76 


11.49 


18.71 


11.58 


22 


23 


19.71 


11.85 


19.66 


11.93 


19.61 


12.02 


19.56 


12.10 


23 


24 


20.57 


12.36 


20.52 


12.45 


20.46 


12.54 


20.41 


12.63 


24 


25 


21.43 


12.88 


21. .37 


12.97 


21.32 


13.06 


'21.26 


13.16 


25 


26 


22.29 


13.39 


22.23 


13.49 


22.17 


13.58 


22.11 


13.68 


26 


27 


23.14 


13.91 


23.08 


14.01 


23.02 


14.11 


22.96 


14.21 


27 


28 124.00 


14.42 


23.94 


14.53 


23.87 


14.63 


23.81 


14.73 


28 


29 


24.86 


14.94 


24.79 


15.04 


24.73 


15.15 


,24.06 


15.26 


29 


30 


25.71 
26.57 


15.45 


25.65 


15.50 


25.. 58 


15.67 


125.51 


15.79 


30 


15.97 


26.. 50 


16.08 


26.43 


16.20 


126.36 


16.31 


31 


32 


27.43 


16.48 


27.36 


16.60 


27.28 


16.72 


S27.21 


16.84 


32 


33 


28.29 


17.00 


28.21 


17.12 


28.14 


17.24 


128.06 


17.37 


33 


34 


29.14 


17.51 


29.07 


17.64 


23.99 


17.76 


128.91 


17.89 


■M 


35 


30.00 


18.03 


29.92 


18.16 


29 . 84 


18.29 


29.76 


18.42 


35 


36 


30.86 


18.. 54 


30.78 


18.68 


.30.70 


18.81 


130.61 


18.94 


36 


37 


31.72 


19.06 


31.63 


19.19 


31.55 


19.33 


131.46 


19.47 


37 


38 


32.57 


19.57 


32.49 


19.71 


32.40 


19.85 


132.31 


20.00 


38 


39 


33.43 


20.09 


33.34 


20.23 


33.25 


20.38 


J33.16 


20.52 


39 


.40 
41 


34.29 


20.60 


34.20 


20.75 


34.11 


20.90 


[34.01 


21.05 


40 


35.14 


21.12 


35.05 


21.27 


34.96 


21.42 


1 34.86 


21.57 


41 


42 


36.00 


21.63 


35.91 


21.79 


35.81 


21.94 


35.71 


22.10 


42 


43 


36.86 


22.15 


36.76 


22.31 


30.66 


22.47 


36.. 57 


22.63 


43 


44 


37.72 


22.66 


37.62 


22.83 


37.. 52 


22.99 


37.42 


23.15 


44 


45 138.57 


23.18 


38.47 


23.34 


38.37 


23.51 


38.27 


23.68 


45 


46 139.43 


23 . 69 


39.33 


23.86 


39.22 


24.03 


39.12 


24.21 


46 


47 40.29 


24.21 


40.18 


24.38 


40.07 


24.. 56 


39.97 


24.73 


47 


48 41.14 


24.72 


41.04 


24.90 


40.93 


25.08 


140.82 


25.26 


48 


49 142.00 


25.24 


41.89 


25.42 


41.78 


25.60 


41.67 


25.78 


49 


50 ! 42.86 


25.75 


42.75 


25.94 


42.63 


26.12 


142.52 


26.31 


50 


..1 

Q 


Dep. 
59] 


Lat. 
3eg. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lut. 


1 
.2 
P 


581 Deg. 


5Qh Deg. 


58k Deg. 



TRAVERSE TABLE 



65 



2 
g 


31 Deg. 


3U Deg. 


31^ Deg. 


311 Deg. 


1 
"51 


Lat. 


Dcp. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 

26.84 


43,72 


26.27 


43.60 


26.46 


43.48 


26.05 


43.37 


52 


44.57 


26.78 


44.46 


26.98 


44.34 


27.17 


44.22 


27.36 


52 


53 


45.43 


27.30 


45.31 


27.49 


45.19 


27.69 


45.07 


27.89 


53 


54 


46.29 


27.81 


46.17 


28.01 


46.04 


28.21 


45.92 28.42 


54 


55 


47.14 


28.33 


47.02 


28.53 


46.90 


28.74 


46.77 28.94 


55 


56 


48.00 


28.84 


47.88 


29.05 


47.75 


29.26 


47.62 


29.47 


56 


57 


48.86 129.36 


48.73 


29.57 


48.60 


29.78 


48.47 


29.99 


57 


58 


49.72 ; 29.87 


49.58 


30.09 


49.45 


30.30 


49.32 


30.. 52. 


58 


69 


50.57 130.39 


50.44 


30.61 


50.31 


30.83 


.50.17 


31.05 


59 


60 
61 


51.43 


30.90 


51.29 


31.13 


51.16 


31.35 
31.87 


51.02 


31.57 


60 
61 


52.29 


31.42 


.52.15 


31.65 


52.01 


51.87 


32.10 


62 


53.14 


31.93 


53.00 


32.16 


.52.86 


32.39 


52.72 


32.63 


62 


63 


54.00 


32.45 


53.80 


32.68 


53.72 


.32.92 


53.57 


33.15 


63 


64 


.54.86 


32.96 


54.71 


33.20 


.54.57 


33.44 


.54.42 


33.68 


64 


65 


55.72 


33.48 


55.. 57 


33.72 


55.42 


33.96 


55.27 


34.20 


65 


66 


56.57 


33.99 


56.42 


34.24 


.56.27 


34.48 


56.12 


34.73 


66 


67 


57.43 


34.51 


57.28 


.34.76 


57.13 


35.01 


56.98 


35.26 


67 


68 


58.29 


35.02 


58.13 


35.28 


57.98 


35.53 


57.82 


35.78 


68 


69 


59.14 


35.54 


58.99 


35.80 


58.83 


36.05 


58.67 


36.31 


69 


70 
71 


60.00 


36.05 


59.84 


36.31 


59.68 


36.57 


59.52 


36.83 


70 
71 


60.86 


36.57 


60.70 


36.83 


60.54 


37.10 


60.37 


37.36 


72 


61.72 


37.08 


61.55 


37.35 


61.39 


37.62 


61.23 


37.89 


72 


73 


62.57 


37.60 


62.41 


37.87 


02.24 


38.14 


62.08 


38.41 


73 


74 


63.43 


38.11 


63.26 


38.39 


63.10 


38.66 


62.93 


38.94 


74 


75 


64.29 


38.63 1 


64.12 


38.91 


63.95 


39.19 


63.78 


39.47 


75 


76 


65.14 


39.14 
39.66 


64.97 


39.43 


64.80 


39.71 


64.63 


39.99 


76 


77 


66.00 


65.83 


39.95 


65.65 


40.23 


65.48 


40.. 52 


77 


78 


G6.86 


40.17 


66.08 


40.46 


66.51 


40.75 


66.33 


41.04 


78 


79 


67.72 


40.69 


67.54 


40.98 


67.36 


41.28 


G7.18 


41.57 


79 


80 
81 


68.57 


41.20 


68.. 39 


41.50 


68.21 


41.80 


68.03 


42.10 


80 
81 


69.43 


41.72 


69.25 142.02 


69.06 142.32 


68.88 


42.62 


82 


70.29 42.23 


70.10 142.54 


69.92 


42.84 


69.73 


43.15 


82 


83 


71.14 


42.75 


70.96 


43.06 


70.77 


43.37 


70.58 


43.68 


83 


84 


72.00 


43.26 


71.81 


43.58 


71.62 


43.89 


71.43 


44.20 


84 


85 


72.86 


43.78 


72.67 


44.10 


72.47 


44.41 


72.28 


44.73 


85 


86 


73.72 


44.29 


73.. 52 


44.61 


73.33 


44.93 


73.13 


45.25 


86 


87 


74.57 


44.81 


74.. 38 


45.13 


74.18 


45.46 


73.98 


45.78 


87 


88 


75.43 


45.32 


75.23 


45.65 


75.03 


45.98 


74.83 


46.31 


88 


89 


76.29 


45.84 


76.09 


46.17 


75.88 


46.50 


75.68 


46.83 


89 


90 
91 


77.15 


46.35 


76.94 

77.80 


46.69 


76.74 


47.02 


76.. 53 


47.36 


90 
91 


78.00 


46.87 


47.21 


77.59 


47.55 


77.38 


47.89 


92 


78.86 


47.38 


78.65 


47.73 


78.44 


48.07 


78.23 


48.41 


92 


93 


79.72 


47.90 


79.51 


48.25 


79.30 


48.59 


79.08 


48.94 


93 


94 


80.. 57 


48.41 


80.36 


48.76 


80.15 


49.11 


79.93 


49.47 


94 


95 


81.43 


48.93 


81.22 


49.28 


81.00 


49.64 


80.78 


49.99 


95 


96 


82.29 


49.44 


82.07 


49.80 


81.85 


50.16 


181.63 


50.52 


96 


97 


83.15 


49.96 


82.93 


50.32 


82.71 


50.68 


182.48 


5:. 04 


97 


98 


84.00 


50.47 


83.78 


50.84 


83.56 


51.20 


183.33 


51.57 


98 


99 


84.86 


.50.99 


84.64 


51.36 


84.41 


51.73 


84.18 


52.10 


99 


100 


85.72 1 51.50 


85.49 


51.88 


85.26 


52.25 


85.04 


62.62 


100 

J 

i 


Dep. 1 Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


59 De?. 


581 Deg. 


58i Deg. 


58} Deg. 



66 



TRAVERSE TABLE. 






32 Deg. 


32i Deg. 


32i Deg. 


321 Deg. 


E 

3 

r 


Lat, 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


"0.85" 


0.53 


0.85 


0.53 


0.84 


0.54 


0.84 


0.54 


2 


1.70 


1.06 


1.69 


1.07 


1.69 


1.07 


1.68 


1.08 


2 


3 


2.54 


1.59 


2.54 


1.60 


2.53 


1.61 


2.52 


1.62 


3 


4 


3.39 


2.12 


3.38 


2.13 


3.37 


2.15 


3.. 36 


2.16 


4 


5 


4.24 


2.65 


4.23 


2.67 


4.22 


2.69 


4.21 


2.70 


5 


6 


5.09 


3.18 


5.07 


3.20 


5.06 


3.22 


5.05 


3.25 


6 


7 


5.94 


3.71 


5.92 


3.74 


5.90 


3.76 


5.89 


3.79 


7 


8 


6.78 


4.24 


6.77 


4.27 


6.75 


4.30 


6.73 


4.33 


8 


9 


7.63 


4.77 


7.61 


4.80 


7.59 


4.84 


7.57 


4.87 


9 


10 
11 


8.48 


5.30 


8.46 


5.34 


8.43 


5.37 


8.41 


5.41 


10 


9.33 i 5.83 


9.30 


-5.W 


9.28 


5.91 


9.25 


5.95 


11 


12 


10.18 


6.36 


10.15 


6.40 


10.12 


6.45 


10.09 


6.49 


12 


13 


11.02 


6.89 


10.99 


6.94 


10.96 


6.98 


10.93 


7.03 


13 


14 


11.87 


7.42 


11.84 


7.47 


11.81 


7.52 


11.77 


7.57 


14 


15 


12.72 


7.95 


12.69 


8.00 


12.65 


8.06 


12.62 


8.11 


15 


16 


13.57 


8.48 


13.53 


8.54 


13.49 


8.60 


13.46 


8.66 


16 


17 


14.42 


9.01 


14.38 


9.07 


14.34 


9.13 


14.30 


9.20 


17 


18 


15.26 


9.54 


15.22 


9.61 


15.18 


9.67 


15.14 


9.74 


18 


19 


16.11 


10.07 


16.07 


10.14 


10.02 


10.21 


15.98 


10.28 


19 


20 


16.96 


10.60 


16.91 


10.67 


16.87 


10.75 


16.82 


10.82 


20 


21 


17.81 


11.13 


17.76 


11.21 


17.71 


11.28 


17.66 


11.36 


21 


22 


18.66 


11.66 


18.61 


11.74 


18.. 55 


11.82 


18.50 


11.90 


22 


23 


19.51 


12.19 


19.45 


12.27 


19.40 


12.36 


19.34 


12.44 


23 


24 


20.35 


12.72 


20.30 


12.81 


20.24 


12.90 ;1 20. 18 


12.98 


24 


25 


21.20 


13.25 


21.14 


13.34 


21.08 


13.43 


21.03 


13.52 


25 


26 


22.05 


13.78 


21.99 


13.87 


21.93 


13.97 


21.87 


14.07 


26 


27 


22.90 14.31 


22.83 


14.41 


22.77 


14.51 


22.71 


14.61 


27 


28 


23.75 


14.84 


23.68 


14.94 


23.61 


15.04 


23.55 


15.15 


28 


29 


24.59 


15.37 


24.. 53 


15.47 


24.46 


15.58 


24.. 39 


15.69 


29 


30 


25.44 


15.90 


25.37 


16.01 


25.30 


16.12 


25.23 


16.23 


30 


31 


26.29 


16.43 


26.22 


16.54 


26.15 


16.66 


26.07 


16.77 


31" 


32 


27.14 


16.96 


27.06 


17.08 


26.99 


17.19 


26.91 


17.31 


32 


33 


27.99 


17.49 


27.91 


17.61 


27.83 


17.73 


27.75 


17.85 


33 


34 


28.83 


18.02 


28.75 


18.14 


28.68 


18.27 


28.60 


18.39 


34 


35 


29.68 


18.55 


29.60 


18.68 


29.52 


18.81 


29.44 


18.93 


35 


36 


30.53 


19.08 


30.45 


19.21 


30.. 36 


19.34 


30.28 


19.48 


36 


37 


31.38 


19.61 


31.29 


19.74 


31.21 


19.88 


31.12 


20.02 


37 


38 


32.23 


20.14 


32.14 


20.28 


32.05 


20.42 


31.96 


20.56 


38 


39 


33.07 


20.67 


32.98 


20.81 


32.89 


20.95 


32.80 


21.10 


39 


40 


33.92 


21.20 


33.83 


21.34 


33.74 

34.58 


21.49 


33.64 


21.64 


40 
41 


41 


34.77 1 21.73 


34.67 


21.88 


22.03 


34.48 


22.18 


42 


35.62 22.26 


35.52 


22.41 


35.42 


22.57 


35.32 


22.72 


42 


43 


36.47 


22.79 


36.37 


22.95 


36.27 


23.10 


.36.16 


23.26 


43 


44 


37.31 


23.32 


37.21 


23.48 


37.11 


23.64 


37.01 


23.80 


44 


45 


38.18 


23.85 


38.06 


24.01 


37.95 


24.18 


37.85 


24.. 34 


45 


46 


39.01 


24.38 


38.90 


24.55 


38.80 


24.72 


38.69 


24.88 


46 


47 


3D. 86 


24.91 


39.75 


25.08 


39.64 


25.25 


39.53 


25.43 


47 


48 


40.71 


25.44 


40.59 


25.61 


40.48 


25.79 


40.37 


25.97 


48 


49 


41.55 


25.97 


41.44 


26.15 


41.33 


26.33 


41.21 


26.51 


49 


50 


42.40 


26.50 


42.29 


26.68 


42.17 


26.86 


42.05 


27.05 


_50 


6 

1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


1 


58 1 


)eg. 


571 Deg. 


67iDeg. 


51 \ Deg. 



TKAVERSE TABLE. 



67 



i 

51 


32 Deg. 


32i Deg. 


32i Deg. 


32J Deg. 




Lat. 


Dep. 1 


Lat. 


Dep. 


Lat. 
43". Of 


Dep.| 

"27.401 


Lat. 


Dep. 


27.03 


43.13 


27.21 


42789 


27,. 59 1 


52 


44.10 


27.56 1 


43.98 


27.75 


43.86 


27.94' 


43.73 


28.13 


52 


53 


4^1.95 


28.09 


44.82 


28.28 


44.70 


28.48 ' 


44.58 


28.67 


53 


64 


45.79 


28 . 62 


45.67 


28.82 


45.54 


29.01 ; 


45.42 


29.21 


54 


55 


46 . 64 


29.15 !| 46.51 


29,35 


46.39 


29.55 


46.26 


29,75 


55 


56 


47.49 


29.68 i; 47.. 36 


29.88 


47.23 


30.09 


47.10 


30.29 


5fi 


57 


48.34 


30.21 ![ 48.21 


30.42 


48.07 


30.63 


47.94 


30.84 


57 


58 


49.19 


30.74 |j 49.05 


30.95 


48.92 


31.16 


48.78 


31.38 


58 


59 


50.03 


31.27 49.90 


31.48 


49.76 


31.70 


49.62 


31.92 


59 


60 
CI 


50 . 88 


31.80 ; 

32.. 33 : 


50.74 


32.02 


50.60 


32.24 


50.46 


32.46 
33.00 


60 
61 


51.73 


51.59 


32.55 


51.45 


32.78 


51.30 


62 


52.58 


32.85 i! 52.44 


33.08 


52.29 


33.31 


52.14 


33.54 


62 


63 


53.43 


33.38, 53.28 


33.62 


53.13 


33.85 


52.99 


34.08 


63 


64 


54.28 


33.91 54.13 34.15 


53.98 


34.39 


53.83 


34.62 


64 


65 


55.12 


34.44 54.97 34.68 


.54.82 


34.92 


54.67 


35.16 


65 


60 


55.97 


34.97 1 55.82 35.22 


55.66 


35.40 


.55.51 


35.70 


66 


67 


.56 . 82 


35.50 56.66 1 35.75 


56.51 


36.00 


56.35 


36.25 


67 


68 


57.67 


36.03 157.51 1 36.29 


57.35 


36.. 54 


57.19 


36.79 


68 


69 


58.52 


36..56i|58.36! 36.82 


58.19 


37.07 


58.03 


37.33 


69 


fi 


.59.36 
60.21 


37.09 ! 59.20 37.35 
37.62 1 60.05 1 37.89 


59.04 


37.61 


58.87 


37.87 


70 
71 


59.88 


38.15 


59.71 


38.41 


72 


61.06 


38.15 : 60.89 1 38.42 


60,. 78 


38.69 


60.. 55 


38.95 


72 


73 


61.91 


38.68 '161.74 138.95 


61.57 


39.22 


61.40 


39.49 


73 


74 


62.76 


39.21 62.58 i 39.49 


62.41 


39.76 


62.24 


40.03 


74 


75 


63.60 


39 . 74 


63.43 i 40.02 


63.25 


40.30 


163.08 


40.57 


75 


76 


64.45 


40.27! 


64.28 


40.. 55 


64.10 


40.83 


63.92 


41.11 


76 


77 


65.30 


40.80 1 


65.12 


41.09 


64.94 


41.37 


64.76 


41.65 


77 


78 


66.15 


41.33 1 


65.97 


41.62 


65.78 


41.91 


6^.60 


42.20 


78 


79 


67.00 


41.86' 


66.81142.10 


66.63 


42.45 


1 66.44 


42.74 


79 


80 
81 


67.84 
68.69 


42.39 
42.92 


67.66 I 42.69 
68.50 1 43.22 


67.47 
68.31 


42.98 


67.28 


43.28 


80 

81 


43.52 


16S.12 


43.82 


82 


69 . .54 


43.45 


69.35! 43.76 


'69.16 1 44.06 


' 68.97 


44.36 


82 


83 


70 . 39 


43.98 


70.20 1 44.29 


70.00 ! 44.60 


; 69.81 


44.90 


83 


84 


71.24 


44.51 1 71.04i 44.82 


70.84 145. 13 


170.65 


45.44 


84 


85 


72.08 


45.04 


71.89 45.36 


171.69 145.67 


! 71.49 


45.98 


85 


86 


72.93 


45.57 


72.73; 45.89 


i 72.53 46.21 


72.33 


46.52 


86 


87 


73.78 


46.10 


73.. 58 


46.42 


173.38 46.75 


73.17 


47.06 


87 


88 


74.63 


46.63 


74.-42 


46.96 


174.22 47.28 


74.01 


47.61 


88 


89 


75.48 


47.16 


75.27 


47.49 


75.06 47.82 


74.85 


48.15 


89 


90 
91 


76.32 

77.17 


47.69 
48 .22' 


76.12 1 48.03 
76.96 i 48.56 


175.91 148.36 


75.09 
176.53 


48.69 


90 
91 


176.75 48.89 


49.23 


92 


78.02 


48 . 75 


77.81 1 49.09 


77.59 49.43 


i 77.38 


49 77 


92 


93 


78.87 


49.28 


78.65 ; 49.63 


78.44 49.97 


178.22 


.50.31 


93 


94 


79.72 


49.81 


79.-50! 50.16 


179.28 50.51 


79.06 


50.85 


94 


95 80.56 


50.34 


1 80.34 


.50 . 69 


80.12 151.04 


i 79.90 


51.39 


95 


96 81.41 


50.87 1 81.19 


51.23 


180.97 1 51.58 


'80.74 


51.93 


96 


97 82.26 


51.40 1:82.04 


51.76 


181.81 ! 52.12 


1 81.58 


.52.47 


97 


98 83.11 51.93 


1 82.88 


52.29 


82.65 152.66 


182.42 


53.02 


98 


99 83.96 .52.46 


83.73 


52.83 


83.50 


53.19 


183.26 


53.56 


99 


1,00 84.80 


52.99 
Lat. 


84.57 


53.36 


184.34 
1 Dep. 


53.73 


84.10 


54.10 


100 

s 

i 

.5 

d 


i 


Dep. 

1 " 


Dep. 


fLat. 


Lat. 


Dep. 


Lat. 


i 58] 


Deg. 


571 Deg. 


57i Deg. 


57i Deg. 



68 



TRAVERSE TABLE. 



o 
1 


33 


Deg. 


33k Deg. 


33i Deg. 


331 Deg. 




Lat. 


Dep. 


Lat. 


Dep. 


'l.V 


Dep. 


Lat. 


Dep. 
~0756 


f 


0.84 


0.54 


0.84 


0.55 


0.83 


0.55 


0,83 


2 


1.68 


1.09 


1.67 


1.10 


1.67 


1.10 


1.6G 


1.11 


2 


3 


2.52 


1.63 


2.51 


1.64 


2.50 


1.C6 


2.49 


1.67 


3 


4 


3.35 


2.18 


3.35 


2.19 


3.34 


2.21 


3.33 


2.22 


4 


5 


4.19 


2.72 


4.18 


2.74 


4.17 


2.76 


4.16 


2.78 


5 


6 


5.03 


3.27 


5.02 


3.29 


5.00 


3.31 


4.99 


3.33 6 


7 


5.87 


3.81 


5.85 


3.84 


5.84 


3.86 


5.82 


3.89! 7 


8 


6.71 


4.36 


6.69 


4.39 


6.67 


4.42 


6.65 


4.44 8 


9 


7.55 


4.90 


7.53 


4.93 


7.50 


4.97 


7.48 


5.00 9 


10 
11 


8.39 


5.45 


8.30 
9.20 


5.48 
6.03 


8.34 
9.17 


5.52 


8.31 
9.15 


5.56 10 
6.11 11 


9.23 


5.99 


6.07 


12 


10.06 


6.54 


10.04 


6.58 


10.01 


6.62 


9.98 


6.67 


12 


13 


10.90 


7.08 


10.87 


7.13 


10.84 


7.18 


10.81 


7.22 


13 


14 


11.74 


7.62 


11.71 


7.68 


11.67 


7.73* 


11.64 


7.78 


14 


15 


12.53 


8.17 


12.54 


8.22 


12.51 


8.28 


12.47 


8.33 


15 


16 


13.42 


8.71 


13.38 


8.77 


13.34 


8.83 


13.30 


8.89 


IB 


17 


14.26 


9.20 


14.22 


9.32 


14.18 


9.38 


14.13 


9.44 


17 


18 


15.10 


9.80 


15.05 


9.87 


15.01 


9.93 


14.97 


10.00 


18 


VJ 


15.93 


10.35 


15.89 


10.42 


15.84 


10.49 


15.80 


10.56 1 19! 


20 


16.77 


10.89 


16.73 


10.97 


16.68 


11.04 
11.59 


16.63 


11.11 


20 


21 


17.61 


11.44 


17.56 


11.51 


17.51 


17.46 


11.67 


21 


22 


18.45 


11.98 


18.40 


12.06 


18.35 


12.14 


18.29 


12.22 


22 


23 


19.29 


12.53 


19.23 


12.61 


19.18 


12.69 


19.12 


12.78 


23 


24 


20.13 


13.07 


20.07 


13.16 


20.01 


13.25 


19.96 


13.33 


24 


25 


20.97 


13.62 


20.91 


13.71 


20.85 


13.80 


20.79 


13.89 


25 


26 


21.81 


14.16 


21.74 


14.26 


21.68 


14.35 


21.62 


14.44 


26 


27 


22.64 


14.71 


22.58 


14.80 


22.51 


14.90 


22.45 


15.00 


27 


28 


23.48 


15.25 


23.42 


15.35 


23.35 


15.45 


23.28 


15.56 


28 


29 


24.32 


1.5».79 


24.25 


15.00 


24.48 


16.01 


24.11 


16.11 


29 


30 
31 


25.16 


16.34 


25.09 


16.45 


25.02 


16.56 


24.94 


16.67 
17.22 


30 
31 


2G.00 


16.88 


25.92 


17.00 


25.85 


17.11 


25.78 


32 


26.84 


17.43 


26.76 


17.55 


26.68 


17.66 


26.61 


17.78 


32 


33 


27.68 


17.97 


27.60 


18.09 


27.52 


18.21 


27.44 


18.33 


33 


34 


28.51 


18.. 52 


28.43 


18.64 


28.35 


18.77 


28.27 


18.89 


34 


3S 


29.. 35 


19.06 


29.27 


19.19 


29.19 


19.32 


29.10 


19.44 


35 


36 


30.19 


19.61 


30.11 


19.74 


30.02 


19.87 


29.93 


20.00 


36 


37 


31.03 


20.15 


30.94 


20.29 


30.85 


20.42 


.30.76 


20.. 55 


37 


38 


31.87 


20.70 


31.78 


20.84 


31.69 


20.97 


31.60 


21.11 


38 


39 


32 71 


21.24 


32.62 


21.. 38 


32.. 52 


21.53 


32.43 


21.67 


39 


40 
41 


33.55 


21.79 


33.45 


21.93 


33.36 
34.19 


22.08 


.33.26 


22.22 


40 


34.39 


22.33 


34.29 


22.48 


22.63 


34.09 


22.78 


41 


42 


35.22 


22.87 


35.12 


23.03 


35.02 


23.18 


34.92 


23.33 


42 


43 


36.06 


23.42 


35.96 


23.58 


35.86 


23.73 


35.75 


23.89 


43 


44 


36.90 


23.96 


36.80 


24.12 


36.69 


24.29 


36.. 58 


24.45 


44 


45 


37.74 


24.51 


37.63 


24.67 


37.. 52 


24.84 


37.42 


25 00 


45 


46 


3S.58 


25.05 


38.47 


25.22 


38.36 


25.39 


38.25 


25.. 56 


46 


47 


39.42 


25.60 


39.31 


25.77 


39.19 


25.94 


39.08 


26.11 


47 


48 


40.28 


26.14 


40.14 


26.32 


40.03 


25.49 


39.91 


26.67 


48 


49 


41.09 


26.69 


40.98 


26.87 


40.86 


27.04 


40.74 


27.22 


49 


50 


41.93 


27.23 


41.81 


27.41 


41.69 


27.60 


41.57 


27.78 


50 


Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


i 

c 


57 Deg. 


56J Deg. 


56i Deg. 


56i Deg. 



travkkse table. 



51 


33 Deg. 


33i Deg. 


33^ Deg. 


331 


Deg. 


i 

51 


Lat. 


Dep. 


Lat. 


Dep: 

27.96 


Lat. 
42.53 


Dep. 

28: 15 


Lat. 


DepT 


42.77 


27.78 


42.65 


42.40 


28.33 


62 


43.61 


28.32 


43.49 


28.51 


43.36 


28.70 


43.24 


28. S9 


52 


53 


44.45 


28.87 


44.32 


29.06 


44.20 


29.25 


44.07 


29.45 


63 


54 


45.29 


29.41 


45.16 


29.61 


45.03 


20.80 


44.90 130.00 


54 


55 


46.13 


29.96 


46.00 


30.16 


45.86 


30.36 


45 . 73 : 30 . 56 


55 


56 


46.97 


30.. 50 


46.83 


30.70 


46.70 


30.91 


46. 56131. 11 


56 


57 


47.80 


31.04 


47.07 


31.25 


47.53 


31.46 


47.39 ! 31.67 


57 


5S 


48.64 


31.59 


48.50 


31.80 


48.. 37 


32.01 


48,23 ! 32.22 


58 


59 


49,48 


32.13 


49.34 


32.35 


49.20 


32.56 


49.06 132.78 


59 


60 
61 


50.32 


32.68 


.50.18 


32.90 


50.03 


33.12 


49.89 1 33.33 


60 


51.16 


.33.22 


51.01 138.45 


.50.87 


33.67 Ij 50.72 1 33. .S9 


61 


62 


.52.00 


33.77 


51.85 33.99 


51.70 


34.22 .51. .55 134.45 


62 


63 


52.84 


34.31 


.52.69 : 34.. 54 


52.53 


34.77 |i 52.38 35.00 


63 


64 


53.67 


34.86 


53.52; 35.09 


,53 . 37 


35.32 53.21 135.56 


64 


65 


54.51 


35.40 


54.36 i 35.64 


54.20 


35.88 54.05 i 36.11 


65 


66 


.55.35 1 35.95 1 


55.19 i 36.19 


55.04 


36.43 54.88 136.67 


66 


67 


56.19 136.49 


56.03 136.74 


55.87 


36.98 65.71 i 37.22 


67 


68 


57.03 i 37.04 


56.87 37.28 


56.70 


37.53 : .56.54 37.78 


68 


69 


57.87 j 37.58 


57.70 


37.83 


57.54 


38.08 1 .57.37 38.33 


69 


70 
71 


58.71 


38.12 


58.54 


38.38 


.58.37 


38.64 


58.20 


38.89 1 
39.45! 


70 

71 


59.55 


38.67 


59.38 


38.93 


59.21 


39.19 


.59.03 


72 


60.38 


39.21 


60.21 


39.48 


60.04 


39 . 74 


59.87 40.00 i 


72 


73 


61.22 


39.76 


61.05 


40.03 


60.87 


40.29 i 60.70 '40.56 1 


73 


74 


62.06 


40.30 


61.89 


40.57 


61.71 


40.84 61.53! 41. Ill 


74 


75 


62.90 


40.85 


62.72 


41.12 


62.. 54 


41.40 


62.36 41.67 


75 


76 


63.74 


41.39 


63.. 56 


41.67 


63.38 


41.95 


63.19 1 42.22 


76 


77 


64.58 


41.94 


64.39 


42.22 


64.21 


42.. 50 


64.02 142.78 


77 


7S 


65.42 


42.48 


65 . 23 


42.77 


65.04 


43.05 


64.85 143.33 


78 


79 


66.25 


43.03 


66.07 


43.32 


65.88 


43.60 


65.69 143.89 


79 


80 
81 


67.09 
67.93 


43.57 


66.90 


43.86 


66.71 


44.15 


66.52 144.45 


80 


44.12 


67.74 


44.41 


67.54 


44.71 


67.35 


45.00 


~8l 


82 


68.77 


44.66 


68.58 


44.96 


68.38 


46.26 


68.18 


45.56 


82 


83 


69.61 


45.20 


69.41 


45.51 


69.21 


45.81 


69.01 


46.11 


83 


84 


70.45 


45.75 


70.25 


46.06 


70.05 


46.36 


69.84 


46.67 


84 


85 


71.29 


46.29 


71.08 


46.60 


70.88 


46.91 


70.67 


47.22 


85 


86 


72.13 


46.84 


71.92 


47.15 


71.71 


47.47 


71.51 47.78 


86 


87 


72.96 


47.38 


72.76 


47.70 


72.55 


48.02 


72.34 148.33 


87 


88 


73.80 


47.93 


73.59 


48.25 


73.38 


48.57 


173.17 148.89 


88 


89 


74.64 


48.47 


74.43 


48.80 


74.22 i 49.12 


[74.00 


49.46 


89 


90 
91 


75.48 


49.02 
49.56 


75.27 
76.10 


49.35 
49.89 


76.05! 49.67 


! 74.83 


.50.00 


90 


76.32 


75.88 i 50.23 


1 75.66 


50.56 


91 


92 


77.16 


.50.11 


76.94 


.50.44 


76.72 1 50.78 


i 76.50 


51.11 


92 


93 


78.00 


50.65 


77.77 


50.99 


77.65 


51.33 


; 77.33 


51.67 


93 


94 


78.83 


51.20 


78.61 i 51.54 


78.39 


51.88 


1 78.16 


52.22 


94 


95 


79.67 


51.74 


79.45 


52.09 


79.22 


52.43 


: 78.99 


62.78 


95 


96 


80.51 


52.29 


80.28 


52.64 


80.05 


52.99 


; 79.82 


63.33 


96 


97 


81.35 


52.83 


81.12 


,53.18 


80.89 


63.64 


180.65 


53.89 


97 


98 


82.19 


53.37 


81.96 


53.73 


81.72 


54.09 


81.48 


54.45 


98 


99 


83.03 


53.92 


82.79 


54.28 


82.55 


54.64 


182.32 


55.00 


99 


100 

1 
.2 


83.87 1 54.46 


183.63 


.54.83 


83.39 


,55.19 


j 83.15 


55.66 


100 


Dep. 


1 Lat. 


D,p. 


Lat. 


Dep. 

■ 


Lat. 


Dep. 


Lat.- 


I 


57 Deg. 


561 Deg. 


56^ Deg. 


56i Deg. 


1; 



70 



TRAVERSE TABLE. 



1 


34 Deg. 


34i Deg. 


34^ Deg, 


341 Deg. 


E' 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 


0.83 


0.56 


0.83 


0.56 


0.82" 


0.57 


0. 82 


0,.57 


1 


2 


1.66 


1.12 


1.65 


1.13 


1.65 


1.13 


1.64 


1.14 


2 


8 


2.49 


1.68 


2.48 


1.69 


2.47 


1.70 


2.46 


1.71 


3 


4 


3., 32 


2.24 


3.31 


2.35 


3.30 


2,27 


3.29 


3,28 


4 


5 


4.15 


2.80 


4.13 


3.81 


4.12 


2,83 


4.11 


2.85 


5 


6 


4.97 


3.36 


4.96 


3.38 


4.94 


3,40 


4.93 


3.42 


6 


7 


5.80 


3.91 


5.79 


3.94 


5.77 


3.96 


5.75 


3.99 


7 


8 


6.63 


4.47 


6.61 


4.50 


6.59 


4.. 53 


6.57 


4.56 


8 


9 


7.46 


5.03 


7.44 


5.07 


7.42 


5.10 


7.39 


5.13 


9 


iO 


8.29 


5.59 


8.27 


5.63 


8.24 


5.66 


8.22 


5.70 
6.27 


10 
11 


11 


9.13 


6.15 


9.09 


6.19 


9.07 


6.23 


9.04 


12 


9.95 


6.71 


9.92 


6.75 


9.89 


6.80 


9.86 


6,84 


12 


13 


10.78 


7.27 


10.75 


7.32 


10.71 


7.36 


10.68 


7,41 


13 


14 


11.61 


7.83 


11.57 


7.88 


1 1 . 54 


7.93 


11.50 


7.98 


14 


1ft 


12.44 


8.39 


12.40 


8.44 


12.36 


8.50 


12.32 


8.. 55 


15 


16 


13.26 


8.95 


13.23 


9.00 


13.19 


9.06 


13.15 


9.12 


16 


17 


14.09 


9.51 


14.05 


9.. 57 


14.01 


9.63 


13.97 


9.69 


17 


IH 


14.93 


10.07 


14.88 


10.13 


14.83 


10.20 


14.79 


10.26 


18 


19 


15.75 


10.62 


15.71 


10.69 


15.66 


10.76 


15.61 


10.83 


19 


20 


16.58 


11.18 


16.53 


11.26 


16,48 


11.33 


16.43 


11.40 


20 


21 


17.41 


11.74 


17. .36 


11.82 


17,31 


11.89 


17.35 


11.97 


21 


22 


18.24 


12.30 


18.18 


12.38 


18.13 


12.46 


18.08 


12.54 


22 


23 


19.07 


12.86 


19.01 


12.94 


18.95 


13.03 


18.90 


13.11 


23 


24 


19.90 


13.42 


19,84 


13.51 


19.78 


13.59 


19.72 


13.68 


24 


25 


20.73 


13.98 


20,66 


14.07 


20.60 


14,16 


30.54 


14.25 


25 


26 


21.55 


14.54 


21.49 


14.63 


21.43 


14.73 


21.36 


14.82 


26 


27 


22.38 


15.10 


22.32 


15.20 


22.25 


15.29 


22.18 


15,39 


27 


28 


23.21 


15 66 


23.14 


15.76 


23.08 


15.86 


23.01 


15,96 


28 


29 


24.04 


16.22 


23.97 


16.32 


23 . 90 


16.43 


23.83 


16.53 


29 


30 


24.87 


16.78 


24.80 


16.88 


24.72 
35.55 


16.99 
17.56 


24.65 


17,10 
17,67 


30 
31 


31 


25.70 


17. .33 


25.03 


17.45 


25.47 


32 


26.53 


17.89 


26.45 


18.01 


36.37 


18.12 


26.29 


18.24 


32 


33 


27.36 


18.45 


27.28 


18,57 


37.30 


18.69 


27.11 


18,81 


33 


34 


28.19 


19.01 


38.10 


19.14 


38.03 


19.26 


27.94 


19,38 


34 


35 


29.02 


19. .57 


28.93 


19.70 


38.84 


19.82 


28.76 


19.95 


35 


36 


29.85 


20.13 


29.76 


30.26 


29.67 


20.39 


29.58 


20.52 


36 


37 


30.67 


20.69 


30,58 


30.83 


30.49 


20.96 


30.40 


21,09 


37 


38 


31.. 50 


21.25 


31.41 


31.39 


31.32 


21.52 


31.22 


21.66 


38 


39 


32.33 


21.81 


32.24 


31.95 


32.14 


33.09 


32.04 


22.23 


39 


40 


33.16 


23.-37 


33.06 


32.51 


.33.97 
33.79 


22.06 


32.87 


22.80 


40 


41 


.33.99 22.93 


33.89 


33.07 


23.23 


33.69 


23.. 37 


41 


42 


34.82 i 23.49 


34.73 


33.64 


34.61 


33.79 


34.51 


23.94 


42 


43 


35.65 


24.05 


35.54 


34.20 


35.44 


24.36 


35.33 


24.51 


43 


44 


36.48 


24.60 


36.37 


24.70 


36.36 


24.92 


36.15 


25.08 


44 


45 


37.31 


25.16 


37.30 


25.. 33 


37.09 


35.49 


36.5,7 


25.65 


45 


46 


38.14 


25.72 


38.03 


25.89 


37.91 


26.05 


37.80 


26.22 


46 


47 


38.96 


26.28 


38.85 1 36.45 


38.73 


26.62 


38.02 [26.79 


47 


48 


39.79 26.84 


39.68,27.01 


39.56 


27.19 


39.44 


37.36 


4S 


49 


40.62 1 27.40 


40.. 50 [27.68 


40.38 


27.75 


40.26 


27.93 


49 


50 


41.45 1 27.96 


41.33 128. 14 


41.31 


28.32 


41.08 


38.50 


50 


6 ' 
1 


Dep, 1 Lat. 


Dep. 1 Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


s 


56] 


Deg. 


551 Deg. 


55A Deg. 


5=4 Deg. 



Xn A VERSE TABLE. 



71 



D 


34Deg. 


34i Deg. 


Mi Deg. 


34J Deg, 


2 

3 



Lat. j Dep. 


Lat. [ Dep. 


Lat. 1 Dep. 


Lat, 1 Dep. 


"51 


42.28 28.52 


42.16 28.70 


42.03:28.89 


41.90 29.07 


'Jl 


52 


43.11 29.08 


42.98 {29.27 


42.85 29.45 


42.73: 29.64 


52 


53 


43.94 29.64: 


43.81 ^29.83 


43.68 .30.02 


43.. 55 30.21 


53 


54 


44.77 30.20 


44.64 i 30.39 


44.50 30.59 


44.37 30.78 


54 


55 


45.60 30.76 1 


45.40 30.95 


45.33 31.15 


45.19 31.35 


55 


56 


46.43 31.31 


46.29 31.52 146.15 31.72 


46.01 31.92 


56 


57 


47.26 31.87 


47.12 32.08 46. 9S 32.29 


40.83 32.49 


57 


58 


48.08 32.43 ': 47.94 ' 32.64 !i 47.80 i 32.85 


47.06 1 33.00 


58 


59 


48.91 32.99 


48.77 33.21 


48.62 33.42 


48.48^33.03 


59 


60 49.74 33.55 1 


49.60 33.77 


49.45 33.98 


49.30 34.20 


60 


61 50.57 34.11 


50.42 34.33 


50.27 34.55 


.50.12 34.77 


^ 


62 


51.40 34.67 1 


51.25 34.89 


51.10 35.12 


50.94 35.34 


62 


63 


52.23 35.23 


52.08 35.46 


51.92 35.68 


51.70 35.91 


63 


64 53.00 35.79 


52.90 36.02 


52.74 36.25 


52.59 30.48 


64 


65 53.89 36.35 


53 . 73 36 . 58 


53.57 36,82 


53.41 1 37.05 


65 


66 54. 72. 36. 9P 


54.55:37.15 


.54.39 [37.38 


54.23 1 37.02 


60 


67 


55.55 37.46 


.55.38 i 37.71 


55.22! 37.95 


55.05| 38.19 


07 


68 


56.37 38.03 


56.21 1 38.27 


56.04! 38.. 52 


.55.87! 38.76 


08 


69 


57.20 38.58 1 


57.03 1 38.83 


56.86 1 39.08 


50.09 


39.33 


69 


70 


58.03 39.14 


57.86 39.40 


57.69 ' 39.65 


57.52 


39.90 


70 


71 


58.86 39.70 


58.69 39.96 


58.51 140.21 


58.34 


40.47 


71 


72 


59.69 40.26 1 


59.51 40. .52 


59.34 140.78 


59.16 


41.04 


72 


73 


60.52 40.82 


60.34(41.08 


60.10 41.35 


59.98 


41.61 


73 


74 


61.35 41.38 


61.17 41.65 


60,99 41.91 


60.80 


42.18 


74 


75 


62.18 41.94 


61.99 42.21 


61.81 142.48 


61.62 


42.75 


75 


76 


63.01 42.50; 


62.82 42.77 


62.63 43,05 


62.45 


43.32 


70 


77 


63.84 43.06 1 


63.65 43.34 


63.46 43.61 63.27 


43.89 


77 


78 


64.66 43.62 


64.47 143.90 


64.28 44.18 1 64.09 


44.46 


78 


79 


65.49 44.18. 


05.30 44.46 


65.11 44.75 


64.91 : 45.03 


79 


80 

81 


66.32^44.74 
67.15 45.29' 


66.13 ;45.02 


65.93 : 45.31 


65.73 45.60 
06.55 40.17 


80 
81 


66.95 45.59 


66.75 45.88 


82 


67.98 45.85 


67.78 46.15 


67.58 1 46.45 


07.37:40.74 


82 


83 


68.81 [46.41 ' 


68.61 146.71 


68.40 


47.01 t 68.20 47.31 


83 


84 


69.64 (46.97 


69.43 47.28 


69.23 


47.58" 69.02 47.88 


84 


85 


70.47 47.53 


70.26 47.84 


70.05 


48.14 


69.84 148.45 


85 


86 


71.30 48.09 


71.09 


48.40 


70.87 


48.71 


70.66! 49.02 


80 


87 


72.13 48.65 


71.91 


48.96 


71.70 


49.28 


71.48 49.59 


87 


88 


72.96 49.21 


72.74 


49.53 


72.52 


49.84 


72.30:50.10 


88 


89 


73.78 149.77 


73.57 


50.09 


73.35 


50.41 


73.13 50.73 


89 


90 
"91 


74.61 50.33 
75.44 i 50.89 


74.39 \ 50.65 


; 74.17 


50,98 


: 73.95! 51.30 


90 
91 


75.22 51.22 


i 75.00 j 51.54 


! 74.77! 51.87 


92 


76.27 51.45 


76.05 ' 51.78 


175.82' 52.11 


1 75.59 1 52.44 


92 


93 


77.10 52.00 


76.87 52.34 


! 76.64 1 52.68 


70.41 ! 53.01 


93 


94 


77.93 52.56 


77.70 , 52.90 


i 77.47 


53.24 


1 77.23! 53.58 


94 


95 


78.76 i 53.12 


78.53 53.47 


78.29 


53.81 


; 78.00 54.15 


95 


96 


79.59 53.68 


79.35 54.03 


79.12 


54.37 


78.88 '54.72 


90 


97 


80.42 154.24 


80.18 : 54.59 


79.94 


54.94 |( 79.70 i 55.29 


97 


98 


81.25 i 54.80 


81.01 1.55.15 


80.70 


55.51 1:80.52 1 ,55.86 


98 


99 


82.07 55.36 


81.83 


55.72 


81.59 


.56.07 |i 81.34 i 56.43 


99 


lOO 

Q 


82.90 55.92 


82.66 


56.28 


82.41 


56.64 


82.16 1 57.00 


100 

g 

.1 




Dep. Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. j Lat. 


56 Deg. 


551 Deg. 


55i Deg. 


55J Deg. 



72 



TRAVEKSB TABLE. 



1 

9 


35 Deg. 


354 Deg. 


35i Deg. 


35i Deg. 





Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 

0.58 


Lat. 


Dep. 


1 


0.82 


0.57 


0.82 


0.,58 


0.81 


0.81 


"0^58" 


1 


2 


1.64 


1.15 


1.63 


1.15 


1.63 


1.16 


1.63 


1.17 


2 


3 


2.46 


1.72 


2.45 


1.73 


2.44 


1.74 


3.43 


1.75 


3 


4 


3.28 


3.29 


3.27 


3.31 


3.26 


3.32 


3.35 


2.34 


4 


5 


4.10 


2.87 


4.08 


2.89 


4.07 


2.90 


4.06 


2.93 


5 


6 


4.91 


3.44 


4.90 


3.46 


4.88 


3.48 


4.87 


3.51 





7 


5.73 


4.01 


5.73 


4.04 


5.70 


4.06 


5.68 


4.09 


7 


8 


6.55 


4.59 


6.53 


4.63 


6.51 


4.65 


6.49 


4.67 


8 


9 


7.37 


5.16 


7.35 


5.19 


7.33 


5.23 


7.30 


5.26 


9 


10 

"ll 


8.19 


5.74 


8.17 


5.77 


8.14 


5.81 
6.39 


8.12 


5.84 
6.43 


10 
11 


9.01 


6.31 


8.98 


6.35 


8.96 


8.93 


12 


9.83 


6.88 


9.80 


6.93 


9.77 


6.97 


9.74 


7.01 


12 


13 


10,65 


7.46 


10.63 


7.50 


10., 58 


7.55 


10.55 


7.60 


13 


U 


11.47 


8.03 


11.43 


8.08 


11.40 


8.13 


11.36 


8.18 


14 


15 


12.29 


8.60 


12.25 


8.66 


12.21 


8.71 


12.17 


8.76 


15 


16 


13.11 


9.18 


13.07 


9.33 


13.03 


9.29 


12.99 


9.35 


16 


17 


13.93 


9.75 


13.88 


9.81 


13.84 


9.87 


13.80 


9.93 


17 


18 


14.74 


10.32 


14.70 


10.39 


14.65 


10.45 


14.61 


10.52 


18 


19 


15.56 


10.90 


15.. 53 


10.97 


15.47 


11.03 


15.42 


11.10 


19 


20 
31 


16.38 


11.47 


16.33 


11. .54 


16.28 


11.61 


lfi.23 
17.04 


11.68 
'12.27 


20 
21 


17.20 


12.05 


17.15 


13.12 


17.10 


12.19 


22 


18.02 


12.62 


17.97 


13.70 


17.91 


12.78 


17.85 


12.85 


22 


23 


18.84 


13.19 


18.78 


13.37 


18.73 


13.36 


18.67 


13.44 


23 


21 


19.66 


13.77 


19.60 


13.85 


19.54 


13.94 


19.48 


14.02 


24 


25 


20.48 


14.34 


20.42 


14.43 


20.35 


14.53 i: 20.29 


14.61 


25 


26(21.30 


14.91 


21.33 


15.0' 


21.171 15.10 


21.10 


15.19 


26 


27 22.12 


15.49 


32.05 


15.58 


21.98 1 15.68 


i21.91 


15.77 


37 


28 


22.94 


16.06 


22.87 


16.15 


22.80 


16.26 


122.72 


16.36 


28 


29 


23.76 


16.63 


23.68 


16.74 


23.61 


16.84 


i 33.54 


16.94 


29 


30 


24.57 


17.21 


24.. 50 
25.32 


17.81 


34.42 


17.42 


1 34.35 


17.53 


30 


■ 31 


25.39 


17.78 


17.89 


25.24 


18.00 


|25.16 


18.11 


31 


32 ! 26.21 


18.35 


26.13 


18.47 


26.05 


18.58 


125.97 


18.70 


33 


33 


27.03 


18.93 


26.95 


19.05 


36.87 


19.16 


36.78 


19.28 


33 


34 


27.85 


19.50 


27.77 


19.63 


27.68 


19.74 


'37.59 


19.86 


34 


35 


28.67 


20.08 


38.58 


20.20 


28.49 


20.33 


128.41 


20.45 


35 


36 


29.49 


20.65 


29.40 


20.78 


29.31 


20.91 


1 29.22 


21.03 


36 


37 30.31 


21.22 


30.22 


21.35 


30.13 


31.49 


30.03 


21.62 


37 


38 i 31.13 


21.80 


31.03 


21.93 


30.94 


22.07 


30.84 


23.20 


38 


39 1 31.95 


22.37 


31.85 


22.51 


31.75 


23.65 


'31.65 


23.79 


39 


40} 32.77 
41 33.. 59 


33.94 


32.67 
33.48 


23.09 
23.66 


33.56 
33.38 


33.33 
33.81 


32.46 
33.27 


23.37 
23.95 


40 
41 


23.. 53 


42 


34.40 


34.09 


34.30 


24.24 


34.19 


34.39 


134.09 


24.54 


42 


43 


35.22 


24.66 


35.12 


24.83 


35.01 


34.97 


1 34.90 


25.12 


43 


44 


36.04 


25.24 


35.93 


35.39 


35.82 


35.55 


35.71 


25.71 


44 


45 


36.86 


25.81 


36 . 75 


35.97 


36.64 


36.13 


36.. 52 


26.29 


45 


46 i 37.68 


26.38 


37.57 


36.55 


37.45 


36.71 


137.33 


26.88 


46 


47 38.. 50 


26.96 II .38.38 


27.13 


38.26 


37.29 


138.14 


27.46 


47 


48 


39.32 


27.. 53 


39.20 


37.70 


39.08 


27.87 


38.96 


28.04 


48 


49 


40.14 


28.11 


40.02 


28.28 


39.89 


28.45 


i39.77 


38.63 


49 


50 


40.96 


28.68_ 


40.83 


38.86 


40.71 


29.04 


140.58 


29.21 


50 


a 

a 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


(5 


55 1 


>eg. 


54} Deg. 


544 Deg. 


54i Deg. 



TJlAVEltSE TABLE. 



73 



1 

51 


35 Deg. 


35i Deg. 


35i Deg. 


351 Deg. 


9 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


1 Dep. 


Lat, 


Dep. 


41.78 


29.25 


41.65 29.43 


41.52^29.62 


41., 39 


29.80 i 51 


52 


42.60 


29.83 


42.47 30.01 


42.33 130.20 


42.20 


30.. 38 .52 


53 


43.43 


.30.40 


43.28 


30.59 


43.15 130.78 


43.01 


30.97 53 


54 


44.23 


30.97 


44.10 


31.17 


43.96 31.36 


43.82 


31.55 54 


55 


45.05 


31.55 


44.92 


31.74 


44.78 31.94 


44.64 


32.13 1 55 


56 


45.87 


32.12 


45.73 


32.32 


45.. 59 132.52 


45.45 


32.72; 50 


57 


46.69 


32.69 


46.. 55 


32.90 


46.40 


33.10 


46.26 


33.,30i 57 


58 


47.51 


33.27 


47.37 


33.47 


47.22 


33.68 


47.07 


33.89 i ,58 


59 


48.33 


33.84 


48.18 


34.05 


48.03 


34.26 


47.88 


34.47 59 


60 
61 


49.15 


34.41 


49.00 


.34.63 


48.85 


34.84 
35.42 


48.69 
49.51 


35.05 60 
35.64" 61 


49.97 


.34.99 


49.82 


35.21 


49.66 


62 


50.79 


35.56 


50.63 


35.78 


50.48 


36.00 Ij 50.32 


.36.22 i 62 


63 


51.61 


36.14 


51.45 


36.36 


51.29 


36.58 i| 51.13 


36. 8i 


63 


64 


52.43 


36.71 


52.27 


36.94 


.52.10 


37.16 51.94 


37.39 


64 


65 


53.24 


37.28 


53.08 


37.51 


.52.92 


37.75 52.75 


37.98 


65 


66 


54.06 


37.86 


53.90 


38.09 


53.73 


38.33 :| 53.56 


38.56 


66 


67 


54.88 


38.43 


54.71 


,38.67 


54.55 


38.91 j.54.38 


39.14 ' 67 


68 


55 . 70 


39.00 


55.53 


39.55 


55.36 


39.49 55.19 


39.73, 68 


69 


56.52 


39.58 


56.35 


39.82 


56.17 


40.07 156.00 


40.31 i 69 


70 

71 


57.34 


40.15 


57.16 
.57.98 


40 40 
40.98 


56.99 
'57.80" 


40.65 


.56.81 


40.90 


70 


58.16 


40.72 


41.23 


57.62 141.48 


71 


72 


.58.98 


41.30 


58.80 


41.. 55 


.58.62 


41.81 


.58.43 1 42.07 


72 


73 


59.80 


41.87 


59.61 


42.13 


'59.43 


42.39 


59 . 24 


42.65 


73 


74 


60 . 62 


42.44 


60.43 


42.71 


60.24 


42.97 


60.06 


43.23 


74 


75 


61.44 


43.02 


61.25 


43.29 


61.06 


43.55 


60.87 


43.82 i 75 1 


76 


62.26 


43.59 


62.06 


43.86 


61.87 


44.13 


61.68 


44.40 76 


77 


63.07 


44.17 


62.88 


44.44 


'62.69 


44.7] 


62.49 144.99 77 


78 


63.89 


44.74 


63.70 


45.02 


63.50 


45.29 


63.30 j 45.57 78 


79 


64.71 


45.31 


64.51 


45.59 


64.32 


45.88 


64.11 46.16 79 


80 
81 


65.53 45.89 


65.33 
66.15 


46.17 
46 . 75 


65.13 


46.46 


64.93! 46.74' 80 
65.74 47.32 > 81 


66.35 


46.46 


65.94 


47.04 


82 


67.17 


47.03 


66.96 


47.33 


66.76 


47.62 


66.55 '47.91 | 82 


83 


67.99 


47.61 


67.78 


47.90 


67.. 57 


48.20 


67.36 I 48.49 1 83 


84 


63.81 


48.18 


68.60 


48.48 


68.39 


48,78 


68 . 1 7 


49.08 t 84. 


85 


69.63 


48.75 


69.41 


49.06 


69.20 


49.36 


08.98 


49.66 85 


86 


70.45 


49.33 


70.23 


49.63 


70.01 


49.94 


69.80 


50.25 1 86 


87 


71.27 


49.90 


71.05 


50.21 170.83 


50.. 52 


70.61 


50.83 87 


88 


72.09 


50 47 


71.86 


50.79 


71.64 


51.10 


71.42 


51.41 


88 


89 


72.90 


51.05 


72.68 


51.37 


72.46 


51.68 


72.23 


.52.00 


89 


90 
91 


73.72 


51.62 


73.50 


51.94 


73.27 

74.08 


.52.26 


73.04 


52.58 


90 
91 


74.54 


,52.20 


74.31 


52.-52 


52.84 173.85 


53.17 


92 


75.36 


52.77 


75.13 


53.10 


74.90 


53.42,174.66 


53.75 


92 


93 


76.18 


.53.341 


75.95 


53.67 


75.71 


54.01 ' 


75.48(54.34 


93 


94 


77.00 


53.92 


76.76 


54.25 


76.. 53 


54.. 59 


76.29 1 54.92 


94 


95 


77.82 


,54.49 


77.58 


54.83 


77.34 


55.17 


77.10 


55.50 


95 


96 


78.64 


55.06 


78.40 


.55.41 


78.16 


55.75 


77.91 


56.09 


96 


97 


79.46 


55.64 


79.21 


.55.98 


7S 97 


56.33 


78.72 


56.07 


97 


98 


80.28 


.56.21 


80.03 


56.. 56 


79.78 


56.91 


79.53 


57.26 


98 


99 


81.10 


56.78 


80.85 


57.14 


80.60 


57.49 


80.35 157.84 


99 


A22 

1 

■a 


81.92 


57.36 


81.66 


57.71 


81.41 


58.07 


81.16 ' 58.42 
Dep. Lat. 


100 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


L«.i 


55 Deg. 


54} Deg. 


54i Dog. 


54i Deg. 


3 



74 



TRAVERSE TABLE. 





CO 

1 

s 

1 


ti6 Deg. 


36i Deg. 


36A Deg. 


361 Deg. 


C 

3 
P 

1 


Lat. Dep. 
~^8T] 0.69 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.81 


0.59 


0.80 


0..59 


0.80 


0.60 


2 


1.62 1.18 


1.61 


1.18 


1.61 


1.19 


1.60 


1 20 


2 


3 


2,43 1.76 


2.42 


1.77 


2.41 


1.78 


2.40 


1.79 


3 


4 


3.24 2.35 


3.23 


2.37 


3.22 


2.38 


3.20 


2.39 


4 


5 


4.05 2.94 


4.03 


2.96 


4.02 


2.97 


4.01 


2.99 


5 


6 


4.85 3.53 


4.84 


3.55 


4.82 


3.57 


4.81 


3.59 


6 


7 


5.66 4.11 


5.65 


4.14 


5.63 


4.16 


5.61 


4.19 


7 


8 


6.47 4.70 


6.45 


4.73 


6.43 


4.76 


6.41 


4.79 


8 


9 


7.28 5.29 


7.26 


5.32 


7.23 


5.35 


7.21 


5.3S 


9 


10 
11 


8.09 


5.88 
6.47 


8.06 


5.91 


8.04 


5.95 


8.01 


5.98 


10 
11 


8.90 


8.87 


6.50' 


8.84 


6.54 


8.81 


6.58 


12 


9.71 7.05 


D.68 


7.10 


9.65 


7.14 


9.61 


7.18 


12 


13 


10. .52 7.64 


10.48 


7.69 


10.45 


7.73 


10.42 


7.78 


13 


14 


11.33: 8.23 


11.29 


8.28 


11.25 


8.33 


11.22 


8.38 


14 


15 


12.14 ! 8.82 


12.10 


8.87 


12.06 


8.92 


12.02 


8.97 


15 


16 


12.94! 9.40 


i 12.90 


9.46 


12.86 


9.52 


12.82 


9.57 


16 


17 


13.75 1 9.99 


13.71 


10.05 


13.67 


10.11 


13.62 


10.17 


17 


18 


14.56 10.58 


14.. 52 


10.64 


14.47 


10.71 


14.42 


10.77 


18 


19 


15.37 j 11.17 


15.32 


11.23 


15.27 


11.30 


15.22 


11.37 


19 


20 
21 


10.18 11.76 


16.13 


11.83 


16.08 
16.88 


11.90 
12.4'9 


16.03 


11.97 


20 
21 


16.99 12. .34 


16.94 


12.42 


16.83 


12.56 


22 


17.80 12.93 


17.74 


13.01 


17.68 


13.09 


17.63 


13.16 


22 


23 


18.61 i 13.52 


18.55 


13.60 


18.49 


13.68 


18.43 


13.76 


23 


24 


19.42 14.11 


19.35 


14.19 


19.29 


14.28 


19.23 


14.36 


24 


25 


20.23 1 14.69 


20.16 


14.78 


20.10 


i4.87 


20.03 


14.96 


25 


26 


21.03 15.28 


20.97 


15.37 


20.90 


15.47 


20.83 


15.56 


26 


27 2i.84 : 15.87 


21.77 


15.97 


21.70 


16.06 


21.63 


16.15 


27 


28 


22.05 116.46 


22.58 


16.56 


22.51 


16.65 


22.44 


16.75 


28 


29 


23.46 i 17.05 


23.39 


17.15 


23.31 


17.25 


23.24 


17.35 


29 


30 
~3l 


24.27 1 17.63 


24.19 


17.74 
18.33 


24.12 


17.84 
18.44 


24.04 17.95 


30 
31 


25.08 18.22 


25.00 


24.92 


24.84 


18.55 


32 25.89 1 18.81 


25.81 


18.92 


25.72 


19.03 


25.64 


19.15 


32 


33 


26.70 1 19.40 


26.61 


19.51 


26.53 


19.63 


26.44 


19.74 


33 


34 


27.51 1 19.98 


27.42 


20.10 


27.33 


20.22 


27.24 


20.34 


34 


35 


28.32,20.57 


28.23 


20.70 


28.13 


20.82 


28.04 


20.94 


35 


36 


29.12 


21.16 


29.03 


21.29 


28.94 


21.41 


28.85 


21.54 


36 


37 


29.93 


21.75 


29.84 


21.88 


29.74 


22.01 


29.65 


22.14 


37 


38 


30.74 


22.34 


30.64 


22.47 


30.55 


22.60 


30.45 


22.74 


38 


39 


31.55 


22.92 


31.45 


23.06 


31.35 


23.20 


31.25 


23.33 


39 


40 


32.36 


23.51 


32.26 


23.65 


32.15 


23.79 


32.05 


23.93 
24". .53 


40 

4T 


33.17 


24.10 


33.06 


24.24 


32.96 


24.39" 


32.85 


42 


33.98 


24.69 


33.87 


24.83 


33.76 


24.98 


33.65 


25.13 


42 


43 


34.79 


25.27 


34.68 


25.43 


34.57 


25.58 


34.45 


25.73 


43 


44 


35.60 


25.86 


35.48 


26.02 


35.37 


26.17 


35.26 


26.33 


44 


45 


36.41 


26.45 


36.29 


26.61 


36.17 


26.77 


36.06 


26.92 


45 


46 


37.21 


27.04 


37.10 


27.20 


36.98 


27.36 


36.86 


27.52 


46 


47 


38.02 


27.63 


37.90 


27.79 


37.78 


27.96 


37.66 


28.12 


47 


48 


38.83 


28.21 


38.71 


28.. 38 


38.59 


28.55 


38.46 


28.72 


48 


49 


39.64 


28.80 


39.52 


28.97 


39.39 


29.15 


39.26 


29.32 


49 


_50 

Q 


40.45 29.39 


40.32 


29.57 


40.19 


29.74 


40.06 


29.92 


50 

1 

s 


Dop. Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


54 Deg. 


5311 


3eg. 


53iDeg. 


53i Deg. 






TEAVKESE TABLE. 



75 



3 

9 
51 


36 Deg. 


36i Deg. 


36i Deg. 


361 Deg. 




1 

? 
"51 


Lat. Dep. 


Lat. 


Dep. 


Lat. 1 Dep 


Lat. 1 Dep. 


i41.26 29.98 


I41.13 


30.16 


41,00 30.34 


40.86:30.51 


52 


42.07 30.66 


i 41.94 


30.75 


41.80 30.93 


41.67 31.11 


52 


53 


42.88 31.15 


'42.74 


31.34 


42.60 31.53 


42.47 i 31.71 


53 


54 


43.69 31.74 


143.55 


31.93 


43.41 132.12 


43.27 [32.31 


54 


55 


'44.50 32.33 ■; 44.35 


32.52 


144.21 132.72 


44.07 1 32.91 


6,5 


5fi 


45.30 32.92 45.16 


33.11 


45.02 ,33.31 j 44.87 133.51 




57 


46.11 33.50 145.97 


33.70 


45.82 j 33.90 45.67 1 34.10 


57 


58 


46.92 34.09 46.77 


34.30 


'46.62 ! 34.50 )l 46.47 134.70 


58 


59 


47.73 .34.68 47.58 


34.89 


: 47.43 ,35 09 i! 47.27 135.30 


59 


61 


48.54 35.27 Ij 48.39 


.35.48 


: 48.23 


35.69 j 48.08 j 35.90 


60 
61 


49.35 35.85 i49. 19 


36.07 


; 49.04 


36.28 


48.88 


36.50 


6-^ 


50.15 36.44 1:50.00 


36.66 


49.84 


36.88 


49.68 


37.10 


62 


63 


50.97 37.03 50.81 


37.25 


50.64 


37.47 


50.48 


37.69 


63 


64 


51.78 37.62 j 51.61 


37.84 


51.45 


38.07 


51.28 


38.29 


64 


65 


52.59 38,21 ' 52.42 


38.44 


52.25 


3S.66 


52.08 


38.89 


65 


66 


.53.40 38.79 | 53.23 


39.03 


! 53.05 


39.26 


62.88 


39.49 


66 


67 


54.20 '• 39.. 38 j 54.03 


39.62 


53.86 


39.85 


53.68 


40.09 


67 


68 


55.01 : 39.97 154.84 


40.21 


54.66 


40.45 


64.49 


40.69 


69 


69 


55.82:40.56 


55.64 


40.80 


55,47 


41.04 


55.29 


41.28 


69 


70 
71 


56.63 41.14 
57.44 41.73 


50.45 


41.39 


56.27 


41.64 


56.09 


41.88 
42.48 


70 

71 


57.26 


41.98 


57.07 142.23 


66.89 


72 


58.25 42.32 ii 58.06 


42.57 


57.88 142.83 


57.69 


43.08 


72 


73 


59.06 42.91 ;| .58.87 


43.17 


58.68 


43.42 


58.49 


43.68 


73 


74 


59.87 43.50 r 59.68 


43.76 


59.49 


44.02 


59.29 


44.28 


74 


75 


60.68 44.08: 


60.48 


44.35 


60.29 


44.61 


60.09 


44,87 


75 


76 


61.49 44.671 


61.29 


44.94 


61.09 


45.21 


60.90 


45.47 


76 


77 


62.29 45.26 


62.10 


45.53 


61.90 


45.80 


61.70 


46.07 


77 


78 


63.10 45.85 


62.90 


46.12 


62.70 


46.40 


62.50 


46.67 


78 


79 


63.91 46.43 


63.71 


46.71 


63.. 50 


46.99 


63.30 


47.27 


79 


80 
81 


64.72 47.02 


64.52 


47.30 


64.31 


47.69 


64.10 


47,87 


80 
81 


65.53 47.61 i 


65.32 


47.90 


65.11 


48.18 


64.90 


48.46 


82 


66.34:48.20; 


66.13 


48.49 


65.92 


48,78 


65.70 


49.06 


82 


83 


67.15 48.79 


66.93 


49.08 


66.72 


49.37 


66.60 


49.66 


83 


84 


67.96 49.37: 


67.74 


49.67 


67.. 52 


49.97 


67.31 


50.26 


84 


85 


68.77 ,49.96 


68.55 


.50.26 


68.33 


50.56 


68.11 


60.86 


85 


86 


69.58 50.55 


69.35 


50.85 


69.13 


51.15 


68.91 


51.46 


86 


87 


70.38 51.14 70.16 


51.44 


69.94 I 51.75, 


69.71 


52.05 


87 


88 


71.19 ,51.73 


70.97 


52.04 


70.74 52.34 


70.51 


52.65 


88 


89 


72.00 52.31 


71.77 


52.63 


71.54 


52.94 


71.31 


53.25 


89 


90 
91 


72.81 52.90; 


72.58 
73.39 


53.22 


72.35 


53.53 


72.11 


.53.86 


90 
-91 


73.62 53.49 


.53.81 


73.15 


54.13 


72.91 


,54.45 


92 


74.43 54.08 


74.19 


54.40 


73.95 


54.72 


73.72 


55.05 


92 


93 


75.24 1.54. 66 


75.00 


54.99 


74.76 


55.32 


74.52 


55.64 


93 


94 


76.05 55.25 i 75.81 


55.. 58 


75.56 


55.91 


75.32 


50.24 


94 


95 


76.86 1 55.84 76.61 


56.17 


76.37 


56.51 


76.12 


56.84 


95 


96 


77.67! 56.43 i| 77.42 


.56.77 


77.17 


67.10 


76,92 


57.44 


96 


97 


78.47 ,57.02 1 78.23 


57.36 


77.97 


57.70 


77,72 


58.04 


97 


98 


79.28 157.60 79.03 


.57.95 


78.78 


58,29 


78,52 


.58.64 


98 


99 80.09 5S.19i 


79.84 


58.54 


79.68 


58.89 


79 32 


59.23 


99 


100 


80.90 ,58.78 I 


80.64 


59.13 


80.39 


59.48 


80.13 


59.83 
Lat. 


100 

5 


1 
1 


Dep. 1 Lat. 

54 Deg. 

1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep 


531 Deg. 


53iDeg. 


53J Deg. 



76 



TRAVERSE TABLK. 



3 


37 Deg. 


37^ Deg. 


37i Deg. 


371 Deg. 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.80 


0.60 


0.80 


0.61 


0.79 


0.61 


0.79 


0.61 


1 


2 


1.60 


1.20 


1.59 


1.21 


1.59 


1.22 


1.58 


1.22 


2 


3 


2.40 


1.81 


2.39 


1.82 


2.38 


1.83 


2.37 


1.84 


3 


4 


3.19 


2.41 


3.18 


2.42 


3.17 


2.43 


3.16 


2.45 


4 


5 


3.99 


3.01 


3.98 


3.03 


3.97 


3.04 


3.95 


3.06 


5 


6 


4.79 


3.61 


4.78 


3.63 


4.76 


3.65 


4.74 


3.67 


6 


7 


5.59 


4.21 


5.57 


4.24 


5.55 


4.26 


5.53 


4,29 


7 


8 


6.39 


4.81 


6.37 


4.84 


6.35 


4.87 


6.33 


4.90 


8 


9 


7.19 


5.42 


7.16 


5.45 


7.14 


5.48 


7.12 


5.51 


9 


10 


7.99 


6.02 


7.96 


6.05 


7.93 


6.09 


7.91 


6.12 


10 
11 


11 


8.78 


6.62 


8.70 


6.66 


8.73 


6.70 


8.70 


6.73 


12 


9.. 58 


7,22 


9.. 55 


7.26 


9.. 52 


7.31 


9.49 


7.35 


12 


13 


10.33 


7.82 


10.35 


7.87 


10.31 


7.91 


10.28 


7.90 


13 


14 


11.18 


8.43 


11.14 


8.47 


11.11 


8.52 


11.07 


8 . 57 


14 


15 


11.98 


9.03 


11.94 


9.08 


11.90 


9.13 


11.86 


9.18 15 j 


16 


12.78 


9.63 


12.74 


9.68 


12.69 


9.74 


12.65 


9.80 lo! 


17 


13.58 


10.23 


13.53 


10.29 


13.49 


10.35 


13.44 


10.41 


17 


18 


14.38 


10.83 


14.33 


10.90 


14.28 


10.96 


14.23 


11.02 


18 


19 


15.17 


11.43 


15.12 


11.50 


15.07 


ll.i>7 


15.02 


1 1 . 63 


19 


20 


15.97 


12.04 


15.92 


12.11 


15.87 
16.66 


12.18 


15.81 


12.24 20 j 


21 


16.77 ! 12.64 


16.72 


12.71 


12.78 


16.60 


12.80 


21 


22 i 17.57; 13.24 


17.51 


13.32 


17.45 


13.39 


17.40 


13.47 


22 


23, 18.37 


13.84 


18.31 


13.92 


18.25 


14.00 


18.19 


14.03 


23 


24 19.17 


14.44 


19.10 


14.53 


19.04 


14.61 


18.98 


14.69 


24 


25 [ 19.97 


15.05 


19.90 


15.13 


19.83 


15.22 


19.77 


15,31 


25 


26 ! 20.76 


15.65 


20.70 


15.74 


20.63 


15.83 


20.56 


15.92 


26 


27 


21.56 


16.25 


21.49 


16.34 


21.42 


16.44 


21.35 


16.. 53 


27 


28 


22.33 


16.85 


22.29 


16.95 


22.21 


17.05 


22.14 


17.14 


2S 


29 


23.16 


17.45 


23.08 


17.55 


23.01 


17.65 


22.93 


17.75 


29 


30 
31 


23.96 
24.76 


18.05 


23.88 


18.16 


23.80 


18.26 


23 . 72 


18.37 


30 
31 


18.06 


24.08 


18.76 


24.59 


18.87 


24.51 


18.9.^ 


32 


25.. 56 


19.26 


25.47 


19.37 


25.39 


19.48 


25.30 


19.59 


33 


33 i 20.35 


19.80 


26.27 


19.97 


26.18 


20.09 


26.09 


20.20 


33 


34 1 27.15 


20.46 


27.06 


20.58 


26.97 


20.70 


26.88 


20.82 


34 


35 1 27.95 


21.06 


27.86 


21.19 


27.77 


21.31 


27.67 


21.43 


35 


36 


28.75 


21.67 


28.66 


21.79 


28.56 


21.92 


28.46 


22.04 


30 


37 


29.55 


22.27 


29.45 


22.40 


29.35 


22.132 


29.26 


22.65 


37 


38 


30.35 


22.87 


30.25 


23.00 


30.15 


23.13 


30.05 


23.26 


33 


39 


31.15 


23.47 


31.04 


23.01 


30.94 


23.74 


30.84 


23.88 


39 


40 
41 


31.95 


24.07 


31.84 


24.21 


31.73 
32 53 


24.35 
24.96 


31.03 


24.49 


40 
41 


32.71 


24.67 


32.64 


24.82 


32.42 


25.10 


42 


33.54 


25.28 


33.43 


25.42 


33 32 


25.57 


33.21 i 25.71 


42 


43 


34.34 


25.88 


34.23 


26.03 


34.11 


26.18 


34.00 '20.33 


43 


44 


35.14! 20.48 


35.02 


26.63 


34.91 


26.79 


34.79 26.94 


44 


45 


35.94 27.08 


35.82 


27.24 


35.70 


27.39 


35..58I27..55 


45 


40 


36.74 


27.68 


36 . 02 


27.84 


36.49 


28.00 


36.37! 28.16 1 46 1 


47 


37.. 54 


28.29 


37.41 


28.45 


37.29 


28.61 


37.16:28.77 1 47 1 


48 


38 . 33 


28.89 


38.21 


29.05 


.38.08 


29.22 


37.95 


29.39 


48 


49 


39.13 


29.49 


39.00 


29.66 


38.87,29.83 


38.74 


30.00 


49 


50 

i 
1 


39.93 


30.09 


39 . 80 


30.26 


39.67 


30.44 


39 . 53 


30.61 


_50 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


1 

.2 


S3 Deg. 


521 Deg. 


52i Deg. 


52i 


Dog. 



TRAVERSE TABLE. 



77 



51 


37 Deg. 


37i Deg. 


37i Deg. 


371 Deg. 


5 
p 


Lat. 


Dcp. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. Dep. 


i 


40.73 


30.69 


40.60 


30.87 


40.46 


31.05 


40, .33 131.22 51 1 


52 


41.53 


31.29 


41.39 


31.48 


41.25 


31.60 


41.12 


31.84 


52 


53 


42.33 


81.90 


42.19 


32.08 


42.05 


.32.26 


41,91 


32.45 


53 


54 


43.13 


32.50 


42.98 


32.69 


42.84 


32.87 


42,70 


33.00 


54 


55 


43.92 


33.10 


43.78 


33.29 


43 . 63 


33.48 


43,49 


33 . 67 


55 


56 


44.72 


33.70 


44.58 


33.90 


44.43 


34.09 


44.28 


34.28 


56 


57 


45.52 


34.30 


45.37 


34.50 


45.22 


34.70 


45.07 


34.90 


57 


58 


46.32 134.91 


40.17 


.35.11 


46.01 


35.31 


45.86 


35.51 


58 


59 


47.12! 35.51 


46.96 


35.71 


46.81 


35 . 92 


46.65 


36.12 


59 


60 
61 


47.92 


36.11 


47.76 


36.32 


47.60 


36 . 53 
37.13 


47.44 


36.73 


60 


48.72 


36.71 


48.. 56 


36.92 


48.39 


48.23 


37.. 35 


"61 


62 


49.. 52 


37.31 


49.. 35 


37.53 


49.19 


37.74 


49.02 


37.96 


62 


63 


50.31 


37.91 


50.15 


38.13 


49.98 


38.. 35 


49.81 


38.57 


63 


64 


51.11 


38.. 52 


50 . 94 


38.74 


50.77 


38.96 


.50.60 


39.18 


64 


65 


51.91 


39,12 


51.74 


39.34 


51.57 


39.57 


51.39 


39.79 


65 


66 


52.71 39.72 


52.54 


39.95 


52.36 


40.18 


52.19 


40.41 


06 


67 


53.51 ] 40.32 


.53.33 


40.55 


53.15 


40.79 


.52.98 


4i.02 


67 


68 


.54.31 140.92 


54.13 


41.16 


53.95 


41.40 


.53.77 


41.63 


08 


69 


.55.11 i41..53 


.54.92 


41.77 


54.74 


42.00 


.54.56 


42.24 


69 


70 
"71 


O5.90 42.13 


55.72 


42.37 


.55.. 53 
.56.33 


42.61 
43.22 


.55.35 


42 86 
43.47 


70 
71 


.56.70 


42 . 73 


56 . 52 


42.98 


56.14 


72 


57.50 


43.33 


,57.31 


43.. 58 


57.12 


43.83 


56 . 93 


44.08 


72 


73 


58.30 


43.93 


58.11 


44.19 


57.91 


44.44 


.57.72 


44.69 


73 


74 


59.10 


44.53 


58.90 


44.79 


.58.71 


45.05 


58.51 


45.30 


74 


75 


59.90 


45.14 


59.70 


45.40 


59 . 50 


45.66 


59.30 45.92 


75 


76 


00.70 


45.74 


60.. 50 


46.00 


60.29 


46.27 


60.09; 48.-53 i 76 8 


77 


61.49 


46.34 


61.29 


46.61 


61.09 


46.87 


60.88 47.14! 77 1 


78 


G2.29 


46.94 


62.09 


47.21 


61.88 


47.48 


61.67 


47.75 i 78 


79 


63.09 47.. 54 


62.88 


47.82 


62.67 


48.09 


62.46 


48.37 i 79 


80 

81 


63.89 148. 15 
64.89 48.75 


63.68 
64.48 


48.42 
49 .03 


63.47 
64.26 


48 , 70 
49.31 


63.26 


48.98 i 80 
49.59 i 81 


64.05 


82 


65.49 49.35 


65.27 


49.63 1 


65.05 


49.92 


64.84 


.50.20 1 82 


83 


66.29 49.95 


66.07 |,50.24i 


65.85 


5.-0.53 


65.63 


.50.81 


83 


84 


67.09 50.55 


66.86 


.50.84 


66.64 51.14 


66.42 


51.43 


84 


85 


67.88 51.15 


67.66 


51 .45 


67.43! 51.74 


67.21 


.52.04 


85 


86 


68.68 51.76 


68.46 


.52.06 


08.23 


.52.35 


68 . 00 


52.65 


86 


87 


69.48 52.36 


09.25 


.52.66 


69.02 


.52.96 


68.79 


.53.26 


87 


88 


70.28 .52.96 


70.05 


53.27 


69.82 


.53.. 57 


69 . .58 


.53.88 


88 


89 


71.08 53. .56 


70.84 


53.87 


70.61 


54.18 


70.37 


54.49 


89 


90 
91 


71.88 54.16 
72.68 .54.77 


71.64 
72.44 


54.48 


71.40 


.54.79 


71.16 


.55.10 


90 


.55.08 


72.20 


.55.40 


71.95 


,55.71 


91 


92 


73.47: 55.37 


73.23 


55.69 


72.99 


56.01 


72.74 


.56.32 


92 


93 


74.27; 55.97 


74.03 


56.29 


73 . 78 


56.61 


73.. 53 


56.94 


93 


94 


75.07' 56.57 


74.82 


56.90 


74.58 


57.22 


74.. 32 


.57., 55 


94 


95 


75.87! 57.17 


75.62 


57.50 


75.37 


57.83 


75.12 


.58.16 


9.5 


96 


76.67 57.77 


76.42 


58.11 


76.16 


58.44 


75.91 


.58.77 


96 


97 


77.47 : 58.38 


77.21 


.58.71 


76.96 


59.05 


76.70 


59.39 


97 


98 


78.27,58,98 


78.01 


59.32 


77.75 


59.60 


77.49 


60.00 


98 


99 


79.06 S .59.. 58 


78.80 ' .59.92 


78.. 54 


60.27 


78.28 60.61 


99 


100 

1 

"5 


79.86 : 60.18 


79.60 60.53 


79.34 


60.88 


79,07 1 61.22 


100 


Dep. 1 Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dcp. Lat, 


1 


53 1 


)e|r. 


521 Deg. 

1 1 


52^ Deg. 


52^ Deg. 



24 



78 



TRAVERSE TABLE. 



5 

3 
p 

T 


38 Deg. 


38i Deg. 


38J Deg. 


38i Dtg. 


J 

1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


D«p. 


0.79 


0.62 


0.79 


0.62 


0.78 


0.62 


0.78 


'~0'.63" 


2 


1.58 


1.23 


1..57 


1.24 


1.57 


1.24 


1.56 


1.25 


2 


3 


2.36' 1.85 




1.86 


2.35 


1.87 


2.34 


1.88 


3 


4 


3.15! 2.46 


3! 14 


2.48 


3.13 


2.49 


3.12 


2.50 4 1 


5 


3.94' 3.08 


3.93 


3.10 


3.91 


3 11 


3.90 


3.13 5I 


G 


4.73 j 3.69 


4.71 


3.71 


4.70 


3.74 


4.68 


3.76 


S 


7 


5. .52, 4.31 


5.50 


4.33 


5.48 


4.36 


5.46 


4.38 


7 


8 


6.30 4.93 


6.28 


4.95 


6.26 


4.98 


6.24 


5.01 


S 


9 


7.09 1 5.54 


7.07 


5.57 


7.04 


5.60 


7.02 


5.63 9 


10 


7.88 


6.16 


7.85 


6.19 


7.83 

8.61 


6.23 


7.80 


6.26 10 


"TT 


8.67 


6.77 


8.64 


6.81 


6.85 


8., 58 


6.89 i 11 


12^ 9.46 


7.39 


9.42 


7.43 


9.39 


7.47 


9.36 


7.51 12 


13 : 10.24 


8.00 


10.21 


8.05 


10.17 


8.09 


10.14 


8.14 13 


14 11.03 8.62 


10.99 


8.67 


10.96 


8.72 


10.92 


8. 70 14 


15! 11.82' 9.23 


11.78 


9.29 


11.74 


9.34 


11.70 


9.39 15 


16 i 12.61 i 9.85 


12.57 


9.91 


12.52 


9.96 


12.48 


10.01 


16 


17 13.40 1 10.47 


13.35 


10.52 


13.30 


10.58 


13.26 


10.64 


17 


18 14.18 1 11.08 


14.14 


11.14 


14.09 


11.21 


14.04 


11.27 


18 


19 ,14.97 11.70 


14.92 


11.76 


14.87 


11.83 


14.82 


11.89 


19 


_20 


15.76 i 12.31 


15.71 


12.38 


15.65 


12.45 


15.60 


12.5?. 


20 


21 


16.55 12.93 


16.49 


13.00 


16.43 j 13.07 


16.38 


13.14"! 21 


22 


17.34 13.54 


17.28 


13.62 


17.22! 13.70 


17.16 


13.77 1 22 


23 


18.12 ' 14.16 


18.06 


14.24 


18.00 


14.32 


17.94 


14.40 23 


24 


18.91 , 14.78 


18.85 


14.86 


18.78 


14.94' 18.72 


15.02 24 


25 


19.70 15.39 


19.63 


15.48 


19.57 


15.56 r 19. .50 


15.65 25 


26 


20.49 ; 16.01 


20.42 


16.10 


20.35 


16.19 : 20.28 


16.27 26 


27 


21.28 1 16.62 


21.20 


16.72 


21.13 


16.81 l'21.06 


16.90 27 


28 


22.06 1 17.24 


21.99 


17.33 


21.91 


17.43!i21.84 


17.. 53 


28 


29 


22.85 17.85 


22 . 77 


17.95 


22.70 


18.05 i 22.62 


18.15 


29 


30 23.64 18.47 


23.56 


18.57 


23.48 


18.68 j 23.40 


18.78 


30 


31 124.43 19.09 


24.34 


19.19 


24.26 


19.30 24.18 


19.40 


31 


32 25.22 i 19.70 


25.13 


19.81 


25.04 


19.92 24.96 


20.03 


32 


33 26.00 20.32 


25.92 


20.43 


25.83 


20.54 1 25.74 


20.66 


33 


34 26.79 20.93 


26.70' 21.05 


26.61 


21.17 1 26. .52 


21.28 


34 


35 27.58,21.55 


27.49 : 21.67 


27.39 i 21.79 1 27.30 


21.91 


35 


36 28.37 : 22.16 


28.27 1 22.29 


28.17 i 22.41 1 28.08 


22.. 53 


36 


37 [29.16 1 22.78 


29.06 


22.91 


28.96 


23.03 28.86 


23.16 ; 37 


38 129.94 1 23.40 


29.84 


23.. 53 


29.74 


23.66 ' 29.64 


23.79 1 38 


39 130.73 124.01 


30.63 


24.14 


30.52 


24.28 , 30.42 


24.41 1 39 


40 31.52; 24.63 

41 : 32.31 125.24 


31.41 


24.76 


31.30 1 24.90 


,31.20 


25.04 1 40 
25.66 41 


32.20 25.38 


32.09 ! 25.. 52 


t 31.98 


42 ' 33.10; 25.86 


32.98 26.00 


32.87 


26.15 


i 32.76 


26.29 42 


43 33.88 26.47 


33.77 26.62 


33.65 


26.77 


33.53 


26.91 43 


44 


34.67 


27.09 


34.55 27.24 


34.43 


27.39 


134.31 


27., 54 ' 44 


45 


35.46 


27.70 


35.34 27.86 


35.22 


28.01 


35.09 


28.17 45 


46 


36.25 


28.. 32 


36.12 128.48 


36.00 


28.64 


35.87 


28.79 46 


47 


37.04 


28.94 


36.91 


29.10 


36. 7S 


29.26 


36 . 65 


29.42: 47 


48 


37.82 


29.. 55 


.37.70 


29.72 


37.57 


29.88 


37.43 


30.04 48 


49 


38.61 


30.17 


38.48 


30.34 


38.35 


30.50 


38.21 


30.67 ; 49 


50 


39.40 30.78 


39.27 


30.95 


39.13 


31.13 


38.99 


31.30 50 


'8 

e 

.2 




Dep. 


Lat. 


Dep. 


Lat. 


Dep, 


Lat. 


Dep. 


Lat. 


;i 


52 Deg. 


5U Deg. 


5H Deg. 


5U Deg. 


1 "i 

is 

1 






TRAVKKSE TABLE. 



79 



o 
5.' 

I 

51 


38 Deg. 


38J Deg. 


384 Deg. 


381 Deg. 


! ^ 


Lat. 


Dep. 


Lat. [ Dep. 


Lat. 


Dep. 


Lat. 

39.77 


Dep. 


3 


40.19 


31.40 


40.05 


31.57 


39.91 


31.75 


3J.92 


51 


52 


40,98 


32.01 


40.84 


.32.19 


40.70 


32.. 37 


40.65 


32.. 55 


52 


53 


41.76 


32.63 


41.62 


32.81 


41.48 


32.99 


41. .33 


33.17 


53 


54 


42.55 


33.25 


42.41 


33.43 


42.26 


33.62 


42.11 


33.80 i 641 


55 


43.34 


33.86 


43.19 


34.05 


43.04 


34.24 


42.89 [ 34.43 .551 


5fi 


44.13 


34.48 


43.98 


.34.67 


43.83 


34.86 


43.67 , 35.05 I 561 


57 


44.92 


35.09 


44.76 


35.29 


44.61 


35.48 


44.45 


35.68! •" 


58 


45.70 


35.71 


45 . 55 


.35.91 


45 . 39 


36.11 


45.23 


36 . 30 1 58 1 


59 


46.49 


36.32 


46.33 


36.. 53 


46.17 


36.73 


46.01 


36.93 


59 


60 
«1 


47.28 


36.94 


47.12 


37.15 


46.96 


37.35 
37.97 


46.79 


37.. 56 
38.18 


60 
61 


48.07 


37.66 


47.90 


37.76 


47.74 


47.57 


«2 


48.86 


38.17 


48.69 


38.38 


48.. 52 


;i8.60 


48.35 


38.81 


62 


fi3 


49.64 


38.79 


49.47 


39.00 


49.. 30 


39.22 


49.13 


39.43 


63 


fi4 


50.43 


39.40 


50.26 


39.62 


.50.09 


39.84 


49.91 


40.06 


64 


65 


51.22 


40.03 


51.05 


40.24 


50.87 


40.46 


50 . 69 


40.68 


65 


66 


52.01 


40.63 


51.8:1 


40.86 


51.65 


41.09 


51.47 


41.31 


66 


67 


62.80 


41.25 


52.62 


41.48 


.52.43 


41.71 


52.25 


41.94 i 67 


6S 


63.58 


41.86 


.53.40 


42.10 


53.22 


42.33 


.53.03 


42.56 i 68 


69 


54.37 


42.48 


54.19 


42.72 


54.00 


42 . 95 


.53.81 


43.19 , 69 


70 
71 


55.16 


43.10 


.54.97 


43.34 


.54.78 


43.. 58 
44.20 


54., 59 


43.81 


70 


55.95 


43.71 


.55.76 


43.96 


,55.57 


55.37 


44 44 


71 


72 


56.74 


44.33 


56.54 


44.57 


56.35 


44.82 


.56.15 


45 07 72 


73 


57.52 


44.94 


57.33 


45.19 


57.13 


45.44 


50.93 


45.59 73 


74 


58.31 


45.56 


58.11 


45.81 


57.91 


46.07 


.57.71 


46.32 74 


75 


59.10 


46.17 


58.90 


46.43 


58.70 


46.69 


.58.49 


46.94 1 75 


76 


59.89 


46.79 


59.68 


47.05 


59.48 


47.31 


59.27 


47.57 1 76 


77 


60.68 


47.41 


60.47 


47.67 


60.26 


47.93 


60 05 


48.20 1 77 


/8 


61.46 


48.02 


61.25 


48.29 


61.04 


48.56 


60 83 


48.82 j 78 


7ft 


62.25 


48.64 


62.04 


48.91 


61.83 


49.18 


61.61 


49.45 I 79 


80 
81 


63.04 


49.25 


62.83 


49.53 : 


62.61 


49.80 


62.39 
63.17 


,50.07 1 80 


63.83 


49.87 


63.61 


50.15 


63.39 


59.42 


50.70 


81 


82 


64.62 


50.48 


64.40 


50 . 77 i 


64.17 


51.05 


63.95 


51.33 


82 


83 165.40 


51.10 


65.18 


51.38 


64.96 


51.67 


64.73 1 51.95 


83 


84 66.19 


51.72 


65.97 


.52.00 


65.74 


52.29 


65.51 


52.. 58 


84 


85 66.98 


52.33 


66 . 75 


.52.62 !! 66.52 


.52.91 


66.29 


53.20 


85 


86 67.77 


.52.95 


67.. 54 


53.54 11 67.30 


53.. 54 


67.07 


53.83 


86 


87 68.56 


.53.56 


68. .32 


53.86 i 68.09 


54.16 


67.85 


54.46 


87 


SR 


69.34 


54.18 


69 . 1 1 


54.48 ij 68.87 


54.78 


68.63 


55.08 


88 


89 


70.13 


54.79 


69.89 


.55.10 ! 69.65 


.55.40 


69.41 


,55.71 


89 


90 
91 


70.92 


55.41 


70.68 


.55.72 ,70.43 


.56.03 


70.19 
70.97 


.56.. 33 


90 
91 


71.71 


56.03 


71.46 


56.34 71.22 


56.65 


5C.96 


92 


72 . 50 


56.64 


72.25 


.56.96 72.00 


.57.27 


71.75 


57.58 


92 


93 


73.28 


57.26 


73.03 


57.58 72.78 


57.89 


72.53 


.58.21 


93 


94 


74.07 


57.87 


73.82 


58.19 73.57 


58.52 


73.31 


58.84 


94 


95 


74,86 


.58.49 


74.61 58.81 74.35 


59.14 


74.09 


.59.46' 95 


96 


75.65 


59.10 


75.39 


59.43 75.13 


59.76 


74.87 


60.09 [ 96 


97 


76.44 


.59.72 


76.18 


60.05 75.91 


60.38 


75.65 


60.71 ! 97 


98 


77.22 


60.. 33 


76.96 


60.67 76.79 


61.01 


76.43 


61.34 98 


99 


78.01 


60.95 


77.75 


61.29 77.48 


61.63 


77.21 


61.97 


99 


100 


78.80 


61.57 


78.53 


61.91 78.26 


62.25 


77.99 


62.69 


1 00 

£ 

c 

1 


.2 


Dep, 


Lat. 


Dep. 


Lat. jl 


Dep. 1 


Lat. 


Dep. 


Lat. 


52 Deg. 


5i| Dog. 


5UDeg. 1 


1 
5UDeg. 



80 



TRAVERSE TABLE. 



a 
1 


39 Deg. 


39J Deg. 


39 i Deg. 


39^ Deg. 




Lat. Dep. 


Lat. 


Dep. 


Lat. 


Dep, 


Lat. 


Dep. 


0.78 0.63 


0.77 


0.63 


"oTtt" 


0,64 


0,77 


0.64 


2 


1.55 1.26 


1.55 


1.27 


1.54 


1,27 


1..54 


1.28 


2 


3 


2.33 1.89 


2.32 


1.90 


2.31 


1,91 


2,31 


1.92 


3 


4 


3.11 2.52 


3.10 


2.53 


3.09 


2.54 


3,08 


2.56 


4 


5 


3.89 3.15 


3.87 


3.16 


3.86 


3,18 


3,84 


3.20 


5 


6 


4. 66 i 3.78 


4.65 


3.80 


4.63 


3.82 


4.61 


3.84 


6> 


7 


5.44' 4.41 


5.42 


4.43 


5.40 


4.45 


5.. 38 


4.48 


7 


8 


6.22 5.03 


6.20 


5.06 6.17 


5.09 


6.15 


5.12 


8 


9 


G.99 5.60 


6.97 


5.69 1! 6.94 


.5.72 


6.92 


5.75 


9 


10 

li 


7.77 


6.29 
6.92 


7.74 


6.33 


7.72 


6.36 


7.69 


6,39 


10 
11 


8.55 


8.52 


6.96 


i 8.49 


7.00 


8.48 


7.03 


12 


9.33 7.55 


9.29 


7.59 


9.26 


7.63 


9.23 


7.67 


12 


13 1 10.10 8.18 


10.07 


8.23 


110.03 


8.27 


9.99 


8.31 


13 


14 i 10.88 8.81 


10.84 


8.86 


10.80 


8.91 


10.76 


8.95 


14 


1.5 


11.66 9.44 


11.62 


9.49 


11.57 


9.. 54 


11. .53 


9.59 


15 


If) 


1'^.43 10.07 


12.39 


10.12 


12. .35 


10.18 


12.30 


10.23 


16 


17 


13.21 10.70 


13.16 


10.76 


13.12 


10.81 


13.07 


10.87 


17 


18 


13.99 11.33 


13.94 


11.39 


13.89 


11.45 


13.84 


11.51 


18 


19 


14.77 11.96 


14.71 


12.02 


14.66 


12.09 


14.61 


12.15 


19 


20 
21 


15.54 12.59 


15.49 


12.65 15.43 


12.72 


15.38 


12.79 


20 

21 


16.32 13.22 


16.26 


13.29 


t 16.20 


13.36 


16.15 


13.43 


22 


17.10 13.84 


J7.04 


13.92 


16.98 


13.99 


16.91 


14.07 


22 


23 


17.87 14.47 


17.81 


14.55 


17.75 


14.63 


17.63 


14.71 


23 


24 


18.65 15.10 


18.59 


15.18 


18., 52 


15.27 


18.45 


15.35 


24 


25 


J9.43 , 15.73 


19.36 


15.82 


19.29 1 15.90 


19.22 


15.99 


25 


26 


20.21 1 16. 3R 


29.13 


16.45 


20.06 16.54 


19.99 


16.63 


20 


27 


20.98 j 16.99 


20. 9i 


17.08 


20.83 


17.17 


20.76 


17.26 


27 


23 


21.70 i 17.62 


21.68 


17.72 


21.61 


17.81 


21.. 53 


17.90 


28 


29 


22.54 1 18.25 


22.46 


18.35 


22.38 


18.45 


22.. 30 


18.54 


29 


30 

-31 


23.31 1 18.88 


23.23 


18.98 


23.15 


19.08 


23.07 

23.83 


19.18 


30 
31 


21.09 


19.51 


24.01 


19.61 


23.92 


19.72 


19.82 


32 


24.87 


20,14 


24.78 


20.25 


24.69 


20.35 


24.60 


20.46 


32 


33 


25.65 


20.77 


25.55 


20.88 


25.46 


20.99 


25 . 37 


21,10 


33 


34 


26.42 


21.40 


26.33 


21.51 


26.24 21.63 


26.14 


21,74 


34 


35 


27.20 I 22.03 


27.10 


22.14 


27.01 


22.26 


26.91 


22,38 


35 


36 


27.98 122.66 


27.88 


22 . 78 


27.78 


22.90 


27.68 


23,02 


3.6 


37 


28.75 i 23.23 


28.65 


23.41 


28.55 


23.53 


28.45 23.66 


37 


38 


29. .53, 23. 91 


29.43 


24.04 


29.32 


24.17 


29.22 124.30 


38 


39 


30.31 ,24. .54 


30.20 


24.68 


30.09 


24.81 


29.98 


24.94 


39 


40 
41 


31.09 25.17 


30.98 


25.31 


30.86 


25.44 
26.08 


30.75 


25.. 58 


40 
41 


31.86 25.80 


31.75 


25.94 


31.64 


31,52 


26.22 


42 


.32.64 26.43 


32 , 52 


26 . .57 


32.41 


26 . 72 


32.29 


26.86 


43 


43 


33.42 27.00 


33.30 


27.21 


33.18 


27.35 


33.06 


27.. 50 


43 


44 


34.19 127.^9 


34.07 


27.84 


33.95 


27.99 


.33.83 


28.14 


44 


45 


.34.97 128.32 


34.85 


28.47 


34.72 


28.62 


34.60 


28.77 


45 


46 


35.75 [28.95 


35 . 62 


29.10 


35.49 


29.26 


35.37 


29.41 


46 


47 


36.. 53 


29.58 1 


30.40 


29.74 


36.27 


29.90 


36.14 


30.05 


47 


48 


37.30 


30.21 


37.17 


30.37 


37.04 


30.. 53 


36.90 


30.69 


48 


49 


38. OS 


30.84 


37.95 


31.00 


37.81 


31.17 


37.67 


31.33 


49 


50 

1 

Q 


38.86 


31.47 


38.72 


31.64 


38., 58 


31,80 


38.44 


31.97 


50 

s 

c 

5 


Dep. 


L... 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


51 Deg. 1 


50|I 


)eg. 


son 


:>og. 


50i I 


3eg. 



TRAVEJiSK TARLE. 



81 



o 

5" 
P 

61 


39 Deg. 


39J Deg. 


39i Deg. 


391 Deg. 


s 
? 
51 


Lat. 1 Dep. 


Lat. 


Dep. 


Lat. 
39.35 


Dep. 


Lat. 


Dep. 


139.63, 32.10 


39.49 32.37 


.32.44 


39.21 


32.61 


62 


; 40.411 32.72 


40.27 32.90 


40.12 


33.08 


39.98 


33.25 


52 


53 


41. 19133. 35 


41.04 33.53 


40.90 


33.71 


40 . 75 


33.89 


53 


54 


141.97 1 33.98 


41.82 34.17 


41.67 


34.35 


41.52 


34.. 53 


54 


55 


43.74 1 34 61 


i 42.59 134.80 


42.44 1,34.98 


42.29 


35.17 


55 


56 


43.52; 35.24 


43.37 


35.43 


43.21 


35.62 


43.06 


35.81 


56 


57 


44. .30, 35.87 


44.14 


36.06 


43.98 


36.26 


43.82 


36.45 


57 


58 


45.07 


36.50 


44.91 


36.70 


44.75 


36.89 


44.59 


37.09 


58 


59 


45.85 


37.13 


45.69 


37.33 


45.53 


37.53 


45.36 


37.73 


59 


60 
61 


48.63 
47.41 


37.76 


46.46 


37.96 


46.30 


38.16 


46.13 


38.37 


60 
61 


38.39 


47.24 


38.60 


47.07 


38.80 


46.90 39 .'01 


62 


48.18 


39.02 


48.01 


39.23 


47.84- 


39.44 


47.67 


39 . 65 


62 


63 


48.96 


39.65 


48.79 


39.86 


48.61 


40.07 


48.44 


40.28 


63 


64 


49.74 


40.28 


49.56 


40.49 


49.38 


40.71 


49.21 


40.92 


64 


65 


,50.51 


40.91 


50,34 


41.13 


.50.16 


41.35 


49.97 


41.56 


65 


66 


51.29 


41.54 


51.11 


41.76 


50.93 


41.98 


50.74 


42.20 


06 


67 


52.07 


42.16 


51.88 


42.39 


51.70 


42.62 


51.51 


42.84 


67 


68 


52.85 


42.79 


52.66 


43.02 


,52,47 


43.25 


52.28 


43.48 


08 


69 


53.52 


43.42 


.53.43 


43.66 


53.24 


43.89 


53.05 


44.12 


69 


70 
71 


.54.40 
55.18 


44.05 


54.21 


44.29 


.54.01 


44.53 
45.16 


63.82 
.54.59 


44 . 76 
45.40 


70 
71 


44.68 


54.98 


44.92 


.54.79 


72 


55 . 95 


45.31 


55.76 


45.55 


55.. 56 


45.80 


55.36 


46.04 


72 


73 


56.73 


45.94 


56.53 


46.19 


56,33 


46.43 


56.13 


46.68 


73 


74 


57.51 


46.57 


57.31 


46.82 


57.10 


47.07 


56.89 


47.32 


74 


75 


68.29 


47.20 


58.08 


47.45 


57.87 


47.71 


.57.66 


47.06 


75 


76 


59.06 


47.83 


58.85 


48.09 


.58.64 


48.34 


.58.43 


48.60 


76 


77 


59.84 


48.46 


59.63 


48.72 


59.42 


48.98 


59.20 


49.24 


77 


78 


60.62 


49.09 


60.40 


49.35 


60.19 


49.61 


59.97 


49.88 


78 


79 


61.39 


49.72 


61.18 


49.98 


60.96 


50.25 


60.74 


50.52 


79 


80 
81 


62.17 


50.. 35 


61.95 


50.62 
51.25 


61.73 
62.60' 


50.89 


61.51 


51.16 


80 
-81 


62.95 


50.97 


"62.73 


51.52 


62.28 


51.79 


82 


63.73 


51.60 


63.50 


51.88 


63.27 


52.16 


63.04 


52.43 


82 


83 


64.. 50 


52.23 


64.27 


52,51 


64.04 


62.79 


63.81 


53.07 


83 


84 


65.28 


52.86 


65.05 


53,15 


64.82 


.53.43 


64.58 


63.71 


84 


85 


66.06 


.53.49 


65.82 


53,78 


65.. 59 


54.07 


65.35 


64.35 


85 


86 


66.83 


54.12 1 


66.60 


54.41 


66.36 


54.70 


66.12 


.54.99 


86 


87 


67.61 


54.75 


07.37 


55.05 


67.13 


55.34 


66.89 


.55.63 


87 


88 


68.. ^9 


55.38 


68.15 


55.68 


67.90 


65.97 


67.66 


66.27 


88 


89 


69.17 


56.01 


68.92 


.56.32 


68.67 


56.61 


68.43 


56.91 


89 


90 
91 


69.94 


56.64 1 


69.70 


56.94 


69.45 
70.22 


57.26 


69.20 


67., 55 


90 
91 


70.72 


57.27 1 


70.47 


57.68 


57.88 


69.96 


58,19 


92 


71.50 


57.90- 


71.24 


58.21 


70.99 


58.52 


70.73 


58.83 


92 


93 


72.27 


68 . 53 : 


72.02 


.58.84 


71.76 


59.16 


71.50 


.59.47 


93 


94 


73.05 


59.16' 


72.79 


59.47 


72.53 


59.79 


72.27 


60.11 


94 


95 


73.83 


59.79 j 


73.57 


60.11 


73.30 


60.43 


73.04 


60.76 


95 


96 


74.61 


60.41 1 


74.34 


60.74 


74.08 


61.06 


73.81 


61.39 


90 


97 


75.38 


61.04 


75.12 


61.37 


74.85 


61.70 


74.68 


62.03 


97 


98 


76.16 


61.67 


75.89 


62.01 


75.62 


62.34 


75.35 


62.66 


98 


99 


76.94 


62.30 


76.66 


62.64 


76.39 


62.97 


76.12 


63.30 


99 


100 

i 

.2 


77.71 


62.93 


77.44 


63.27 


77.16 


63.61 


76.88 


63.94 


100 

s 

5 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


51 Deg. 


501 Deg. 


50i Deg. 


50i Deg. 



82 



TRAVERSE TABLE 



1 


40 Deg. 


m Deg. 


40i Deg. 


40.1 Deg. 


? 

1 


Lat. 1 Dpp. 1 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 

0T65 


0.76 


0.65 


0.76 


0.65 


0.76 


2 


1.53 1.29 


1.53 


1.29 


1..52 


1.30 


1.52 


1.31 


2 


3 


2.30 


1.93 


2.29 


1.94 


2.28 


1.95 


2.27 


1.96 


3 


4 


3.06 


2,57 


3.05 


2.58 


3.04 


2.60 


3.03 


2,61 


4 


5 


3.83 


3.21 


3.82 


3.23 


3.80 


3.25! 


3.79 


3.26 


5 


6 


4.60 


3.80 


4.58 


3.88 


4.. 56 


3.90 1 


4,55 


3-92 


6 


7 


5.36 


4.50 


5.34 


4.52 


5.32 


4.55 


5,30 


4.57 


7 


8 


6.13 


5.14 


6.11 


5.17 


6.08 


5.20 


6.06 


6.22 


8 


9 


6.89 


5.79 


6.87 


5.82 


6.84 


5.84 


6.82 


5.87 


9 


10 
11 


7.66 


6.43 
7.07 


7.63 


6.46 


7.60 


6.49 
7.14 


7.58 
8.33 


6,53 

7,18" 


10 
11 


8.43 


8.40 


7.11 


8.36 


12 


9.19 


7.71 


9.16 


7.75 


9.12 


7.79 1 


9.09 


7.83 


12 


13 


9.96 


8.36 


9.92 


8.40 


9.89 


8.44 1 


9.85 


8,49 


13 


14 


10.72 


9.00 


10.69 


9.05 


10.65 


9.09 I 


10.61 


9,14 


14 


15 j 


11.49 


9.64 


11.45 


9.69 


11.41 


9.74 


11.36 


9,79 


15 


16 


12.26 


10.28 


12.21 


10.34 


12.17 


10.39 


12.12 


10.44 


16 


17 


13.02 


10.93 


12.97 


10.98 


12.93 


11.04! 


12.88 11.10 


17 


18 


13.79 


11.57 


13.74 


11.63 


13.69 


11.69 : 


13.64 


11.75 


18 


19 


14. .55 


12.21 


14.50 


12.28 


14.45 


12.34 


14.39 


12.40 


19 


20 


15.32 


12.86 


15.26 


12.92 


15.21 


12.99 


15.15 


13.06 


20 


21 


16.09 


13.50 


16.03 


13.57 


15.97 


13.64 


15,91 


13.71 


21 


22 


16.85 


14.14 


16.79 


14.21 


16.73 


14.29 


16,67 


14.36 


22 


23 


17.62 


14.78 


17.55 


14.86 


17.49 


14.94 


17.42 


15.01 


23 


24 


18.39 


15.43 


18.32 


15.51 


18.25 


15.59! 


18.18 


15.67 


24 


25 


19.15 


16.07 


19.08 


16.15 


19.01 


16.24 


18.94 


16.32 


25 


2R 


19.92 


16.71 


19.84 


16.80 


19.77 


16.89 


19.70 


16.97 


26 


27 


20 . 68 


17.36 


20.61 


17.45 


20.53 


17. ,54 


20.45 


17.62 


27 


28 


21.45 


18.00 


21.37 


18.09 


21.29 


18.18 


21.21 


18.28 


28 


29 


22.22 


18.64 


22.13 


18.74 


22.05 


18.83 


21.97 


18.93 


29 


30 
31 


22.98 19.28 


22.90 
23.66 


19.38 


22.81 


19.48 
20.13 


22.73 
23.48 


19.. 58 
'20.24 


30 
31 


23 . 75 


19.93 


"20703 


23.57 


32 


24.51 


20 . 57 


24.42 


20.68 


24.33 


20.78 


24.24 


20.89 


32 


33 


25.28 


21.21 


25.19 


21.32 


25.09 


21,43 


25.00 


21.54 


33 


34 


20.05 


21.85 


25.95 


21.97 


25.85 


22.08 


25.76 


22.19 


34 


35 


26.81 


22.50 


26.71 


22.61 


26.61 


22.73 


26.51 


22.85 


35 


30 


27.58 


23.14 


27.48 


23.26 


27.37 


23.38 


27,27 


: 23.50 


36 


37 


28.34 


23.78 


28.24 


23.91 


28.13 


24.03 


28,03 


24,15 


37 


38 


29.11 


24.43 


29.00 


24.55 


28.90 


24.68 


28,79 


j 24.80 


38 


39 


29.88 i 25.07 


29.77 


25.20 


29.66 


25.33 


29,54 


1 25,46 


39 


40 


30.64 25.71 


30.53 


25.84 


30.42 


25.98 


,30,30 


i 26 , 1 1 


40 


41 


31.41 126.35 


31.29 


26.49 


31.18 


26.03 


31,06 


! 26,76 


41 


42 


32.17; 27.00 


32.06 


27.14 


31.94 


27.28 


31,82 


27.42 


42 


43 


32.94 I 27.64 


32.82 


27.78 


32.70 


27.93 


132,58 


28.07 


43 


44 


33.71 28.28 


33.58 


28.43 


33.46 


28.58 


33.33 


28.72 


44 


45 


34.47 28.93 


34.35 


29.08 


34.22 


29.23 


t 34,09 


' 29.. 37 


45 


46 


35.24 29.57 


35.11 


29.72 


34.98 


29.87 


34,85 


30.03 


46 


47 


36.00 30.21 


35.87 


30.37 


35.74 


30.52 


35,61 


! 30.68 


47 


48 


36.77 1 30.85 


36.64 


31.01 


36.50 


31.17 


36,36 


! 31.33 


48 


49 ' 37.54' 31.50 


37.40 


31.66 


37.26 


31.82 


37,12 


31.99 


49 


50 j 38.30 1 32.14 


^.16 


32.31 


38.02 


32,47 


37,88 


,J^2.64 


_5J 


e 
It 

i5 


Dep. 1 Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


1 Lat. 




50 Deg. 


49J Deg. 


49i Deg. 


m Deg. 



TRAVERSE TABLE. 



83 



3 


40 Deg. 


40i Deg. 


40h Deg. 


401 Deg. 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 

38.78 


Dep. 


Lat. 
38.64 


Dep. 


39.07 


32.78 


33.92 


32.95 


.33.12 


33.29 51 


52 


39.83 


33.42 


39.69 


33.60 


39.54 


33.77 


,39.39 


33.94 .52 


53 


40.60 ' 34.07 


40.45 


34.34 


40.30 


34.42 


40.15 


,34.60 53 


51. 


41.37 


34.71 


41.21 


34.89 


41.06 


35 . 07 


40.91 


35 . 25 i 54 


55 


42.13 


3.',. 35 


41.98 


35 . 54 


41.82 


35.72 


41.67 


35.90 , .55 


56 


42.90 


36.00 


42.74 


36.18 


42.. 58 


36.37 


42.42 


36.-55 1 56 


57 


43.66 


36 . 64 


43 . 50 


36.83 


43.34 


37.02 


43.18 ' 37.21 


57 


58 


44.43 


37.23 


44.27 


37.48 


44.10 


37.67 


43.94 


37.86 


58 


59 


45 . 20 


37.92 


45.03 


33.12 


44.86 


3«..32 


44.70 


33.51 


59 


f.O 


45 . 96 


38.57 


45 . 79 


38 . 77 


45.62 138.97 


45.45 


39.17 


60 


■ P,[ 


46.73 


39.21 


46.56 


39.41 


46 . 33 1 39 . 62 


46.21 


39.82 


61 


62 


47.49 


39.85 


47.32 


40.06 


47.15 


40.27 


46.97 


40.47 


62 


63 


48.26 


40.50 


48.08 


40.71 


47.91 


40 . 92 


47.73 


41.12 


63 


64 


49.03 


41.14 


48.85 


41.35 


48.67 


41.56 


48.48 


41.78 


64 


65 


49 . 79 


41.78 


49.61 


42.00 


49.43 


42.21 


49.24 


42.43 


65 


66 


50.56 


42.42 


50.37 


42.64 


.50,19 


42.86 


50.00 


43.08 


66 


67 


51.32 


43.07 


51.14 


43.29 


50.95 


43.51 


50.76 


43 . 73 


67 


6S 


52.09 


43.71 


51.90 


43.94 


51.71 


44.16: 


51.51 


44.39 


68 


69 


52.86 


44.35 


52.66 


44.53 


.52.47 


44.81 j 


.52.27 


45.04 


69 


70 

71 


.53 . 62 


45.00 


53.43 


45.23 


53.23 
.53.99 


45.46 : 


53.03 


45.69 


70 


.54.39 


45 . 64 


54.19 


45.87 


46.11 i 


,53.79 


46.35 


71 


72 


55.16 


46.28 


.54.95 


46.52 


,54.75 


46.76 i 


54., 54 


47.00 


72 


73 ! 55.92 


46.92 


55.72 


47.17 


.55.51 


47.41 


55.30 


47.65 


73 


74 


.56.69 


47.57 


56.48 


47.81 


56.27 


48.06 1 56.06 


48., 30 


74 


75 


57.45 


48.21 


57.24 


48.46 


57.03 


48.71 


56.82 


48.96 


75 


76 


58.22 


48.85 


58.01 


49.11 


5? . 79 


49.36 


57.57 


49.61 


76 


77 


.58.99 


49.49 


.58.77 


49.75 


58.55 


.50.01 


,58.33 


50.26 


77 


78 


59.75 


.50.14 


59,. 53 


.50.40 


59.31 


,50.66 


59.09 


50.92 


73 


79 


60.. 52 


50.78 


60.30 


51.04 


60.07 


51.31 


.59.85 


51., 57 


79 


80 
81 


61.28 


51.42 


61.06 


51.69 


60.83 
'6i.59 


51.96 
.52.61 


60.61 


,52.22 


80 


62.05 


.52.07 


61.82 


52 . 34 


61.36 


52.87 


81 


82 i 62 . 82 


52.71 


62.59 


.52.98 


62.35 


.53.25 


62.12 


53.53 


32 


83 1 63.58 


.53.35 


63.35 


53.63 


63.11 


.53.90 


62.88 


.54.18 


83 


84 1 64.35 


53 . 99 


64.11 


.54.27 


63.87 


54.. 55 


63.64 


54.83 


84 


85 


65.11 


54.64 


64.87 


.54.92 


64-63 


,55.20 


64.39 


55.48' 85 1 


86 


65.88 


,55.28 


65.64 


55.57 


65- 39 


55.85 


65.15 


56.14 


86 


87 


66.65 


55.92 


66.40 


56.21 


66.16 


56 . .50 


65.91 


56.79 


87 


88 


67.41 


56 . 57 


67.16 


.56 . 86 


66.92 


57.15 


66.67 


.57.44 


i'8 


89 


68.18 


57.21 


67.93 


57 . ,50 


67.68 


57.80 


67.42 


58.10 


89 


90 
"91 


68.94 


57.85 


68.69 
69.45 


58.1.5 


68.44 


58.45 


68.18 


58 . 75 


90 


69.71 


58.49 


58.80 1 


69.20 


59.10 


68.94 


59.40 


91 


92 


70.48 


59.14 


70.22 


59 . 44 1 


69.96 


59.75 


69.70 


60.05 


92 


93 


71.24 


59.78 


70.98 


60.09 


70.72 


60.40 


70.45 


60.71 


93 


94 


72.01 


60.42 


71.74 


60.74 


71.48 


61.05 


71.21 


61.36 


94 


95 


72.77 


61.06 


72.51 


61.33 


72.24 


61.70 


71.97 


62.01 


95 


93 73.54 


61.71 


73.27 


62.03 


73.00 


62., 35 


72.73 


62.66 


96 


97 74.31 


6-2.35 


74.03 


62.67 


73.76 


63.00 


73.48 


63.32 


97 


1)8 1 75.07 


62.99 


74.80 


63.32 


74.52 


63.65 


74.24 


63.97 


98 


99 i 75.84 


63 . 64 


75.56 


63.97 


75.28 


64.30 


75.00 


64.62 


99 


l.)0 


76.60 


64.28 


76.32 


64.61 


76.04 


64.94 


75.76 
Dep. 


65.23 


100 

g 

c 

"to 

O 


9 
s 


Dep. 


Lat. 


Dep. 


Lat. 

1 


Dep. 


Lat. 


Lat. 


5 


50 Deg. 


491 Deg. 


49 h Deg. 


49i Deg. 



84 



TRAVERSE TABLE. 



5 

i 

1 


41 Deg. 


4U Deg. 


4U Deg. 


411 Deg. 


i 
1 


Lat. 1 Dep. 


Lat. 


Dep. 
0.C6 


Lat. 


Dep. 


Lat. 


Dep. 
0.67 


0.75 1 0.6fi 


0.75 


1 0.75 


0.66 


0.75 


2 


1.51 : 1.31 


1.50 


1.32 


1..50 


1.33 


1.49 


1.33 


2 


•3 


2.26 1.97 


2.26 


1.98 


2.25 


1.99 


2.24 


2.00 


3 


4 


3.02 2.62 


3.01 


2.64 


3.00 


2.65 


2.98 


2.66 


4 


5 


3.77 3.28 


3.76 


3.30 


i 3.74 


3.31 


3.73 


3.33 


5 


6 


4.53 : 3.94 


4.51 


3.90 


4.49 


3.98 


4.48 


4.00 


6 


7 


5.23; 4.50 


5.26 


4.62 


5 . 24 


4.64 


5.22 


4.66 


7 


8 


6.04 1 5.25 


6.01 


5.27 


5 99 


5.30 


5.97 


5.33 


8 


9 


6.79 5.90 


6.77 


5.93 


6.74 


5.96 


6.71 


5.99 


9 


10 


7.55 6.56 


7.52 


6.59 


7.49 


6.63 


7.46 


6.66 


10 


11 


8.30 7.22 


8.27 


7.25 


8.24 


7.29 


8.21 


7.32 


11 


12 


9.06 7.87 


9.02 


7.91 


8.99 


7.95 


8.95 


7.99 


12 


13 


9.81 


8.53 


9.77 


8.57 


9.74 


8.61 


9.70 


8.06 


13 


14 


10.57 


9.18 


10.53 


9.23 


10.49 


9.28 


10.44 


9.32 


14 


15 


11,32 


9.84 


11.28 


9.89 


11.23 9.94 


11.19 


9.99 


15 


16 


12.08 


10., 'iO 


12.03 


10.55 


11.98 10.60 


11.94 


10,65 


16 


17 


12.83 


11.15 


12.78 


11.21 


12.73 


11.26 


12.68 


11.32 


17 


18 


13.58 


11.81 


13.53 


11.87 


13.48 


11.93 


13.43 


11.99 


1.8 


19 


14.34 


12.47 


14.28 


12.. 53 


14.23 


12.59 


14.18 


12.65 


19 


20 


15.09 13.12 1 


15.04 


13.19 


14.98 


13.25 


14.92 


13.32 


20 


21 


15.85 13.78 1 


15.79 


13,85 


15.73 


13.91 


15.67 


13.98 


2l 


22 


16.60 14.43 1 


16.54 


14.51 


16.48 


14.58 


16.41 


H.65 


22 


23 


17.36 15.09 


17.29 


15.16 


17.23 


15.24 


17.16 


15.32 


23 


24 


18.11 15.75 ' 


18.04 


15.82 


17.97 


15.90 


17.91 1 15.08 


24 


25 


18.87 , 16.40 


18.80 


16.48 


18.72 


16.57 


18.65 


16.65 


25 


26 


19.02; 17.06 


19.55 


17.14 


19.47 i 17.23 1 


19.40 


17.31 


26 


27 


20.38 .. 17.71 


20.30 


17.80 


20.22 1 17.89 


20.14 


17.98 


27 


28 


21.13 18.37 


21.05 


18.46 


20.97 1 18. .55 


20.89 


18.64 


28 


29 


21.89 19.03 


21.80 


19.12 


21.72 1 19.22 


21.64 


19.31 


29 


30 


22.64 19.68 


22.56 


19.78 


22.47 1 19.88 


22.38 


19.98 


30 


31 


23.40 20.34 


23.31 


20.44 


23.'22 


20.54 


23 . 13 


20.64 


3! 


32 


24.15 20.99 


24.06 


21.10 


23.97 


21.20 


23.87 


21.31 


32 


33 


24.91 21.65 


24.81 


21.76 


24.72 


21.87 


24.62 


21.97 


33 


34 


25.66 22.31 


25.56 


22.42 


25.4i5 


22.. 53 


25.37 


22 . 64 


34 


35 


26.41 22.06 


26.31 


23.08 


26.21 


23.19 


26.11 


23.31 


35 


36 


27.17 23.62 


27.07 


23.74 


26.96 123.85 


26.86 


23.97 


36 


37 


27.92 124.27 


27.82 


24.40 


27.71 


24.. 52 


27.60 


24.64 


37 


38 


28.68 ,24.93 


28.57 


25.06 


28.46 


25.18 


28.35 


25.30 


38 


39 


29.43 25.59 


29.32 


25.71 


29.21 


25.84 


29.10 


25.97 


39 


40 


30.19 26.24 


30.07 


26 . 37 


29.96 


26.50 


29.84 


26.64 


40 


41 


30.94 26.90 


30.83 127.03 


"30.71 


27.17 


.30.59 


27 . SO 


41 


42 


31.70 27. .55 


31. .58 t 27.69 


31.46 


27.83 


31.33 


27.97 


42 


43 


32.45 28.21 


32.33 [28.35 


32.21 


28.49 


.32.08 


28.63 


43 


44 


33.21 28.87 


33.08 ! 29.01 


32.95 


29.16 


32.83 


29.30 


44 


4ft 


33.96 29.. 52 


33.83 1 29.67 


33.70 


29.82 


33.57 


29.97 


45 


46 


34.72 ,30.18 


34.-58 


30.33 


34.45 


30.48 


34.32 


30.63 


46 


47 


35.47 130.83 


35.34 


30.99 


35 . 20 


31.14 


35.06 


31.30 


47 


48 


36.23 31.49 


36.09 


31.65 


35.95 


31.81 


35 . 8 1 


31.96 


48 


49 


36.98 32.15 


36.84 


32.31 


36.70 


32.47 


36.56 


32.63 


49 


50 

i 


37.74 32.80 


37.59 


32.97 


3V.45 


33.13 


37.30 


33.29 


50 

c 
B 


Dep. 1 Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


49 Deg, 


48J Deg. 


m Dog. 


48i Deg. 



TRAVKRSE TABLE. 



85 



3 


41 Deg, 


4U Deg. 


1 41i Deg. 


411 Deg. 




Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep, 


Lat. 


Dep. 


? 


33.49 


33.46 


.38.34 


33.63 


.38.20 


33,79 


,33.05 


33.96 


"51 


52 


39.24 


34.12 


39.10 


34.29 


33 . 95 


34.46 


33 . 79 


34.63 .52 1 


53 


40.00 


34.77 


39.85 


34.95 


39.69 


35.12 


39.-54 


35,29 .53! 


54 


40 . 75 


35.43 


40.60 


35.60 


40.44 


35.78 


40.29 


35,98 1 .541 


55 


41.51 


36. OS 


41,35 


36 . 26 


41.19 


36.44 


41,03 


36 . 62 


55 


56 


42.26 


36.74 


42.10 


36.92 


41.94 


37.11 


41,78 


37.29 


56 


57 


43.02 


37.40 


42.85 


37.58 


42.69 


37.77 


42.. 53 


37.96 


57 


53 


43.77 


38.05 


43.61 38.24 


43.44 


38.43 


43.27 


38 . 62 


58 


59 


44.. 53 


38.71 


44.38 38.90 


44.19 


39.09 


44.02 


39.29 


59 


61 


45.28 


39.36 


45.11 1 39.56 


44.94 


39.76 


44.76 


39.95 


60 
61 


46 . 04 


40.02 


45.86 1 40,22 


45.69 


40.42 


45.51 


40.62 


62 


46.79 


40.68 


46.61 1 40.88 


46.44 


41.08 


46.26 


41.23 


62 


63 


47.55 


41.33 


47.37 1 4L.,54 


47.18 


41,75 


47.00 


41.05 


63 


64 


48.30 


41.99 


48. 12 142.20 


47.93 


42.41 


47.75 


42.62 


64 


65 


49.06 


42.64 


48.87 ' 42.86 


48.68 


43,07 


48.49 


43.28 


65 


66 


49.81 


43.30 


49.62 43.. 52 


49.43 


43 , 73 


49.24 j 43.95 


66 


(57 


50.57 


43.96 


50.37 i44,l8 


50.18 


44,40 


49.99 1 44.61 


67 


68 


5 1 . 32 


44.61 


51.13 i 44.84 


.50.93 


45,08 


50.73 45.28 


68 


69 


52.07 


45.27 


51.88 


45.49 


51.63 


45.72 


51.48 


45.95 


69 


70 
71 


52.83 


45.92 


52 , 63 


46.15 


.52.43 


46.38 
47.05 


52.22 


46.61 

47.28 


70 
"71 


.53.58 


46.58 


53.38 


46.81 


.53.18 


.52.97 


72 


.54.34 


47.24 


54.13 


47.47 


.53.92 


47.71 


53.72 


47.94 


72 


73 


55.09 


47.89 


54.88 


48.13 


54.67 


48.37 


.54.46 


48.61 


73 


74 


.55.85 


48.55 


55.64 


48.79 


55.42 


49.03 


55.21 


49.28 


74 


75 


56.60 


49.20 


.56.39 


49.45 


,56.17 


49.70 


.55.95 


49.94 


75 


76 


57.36 


49.86 


57.14 


50.11 


56.92 


.50.. 36 


56 . 70 


.50.61 


76 


77 


58,11 


50,52 


.57.89 


50.77 


.57,67 


51.02 


57.45 51.27 


77 


78 


58.87 


51.17 


58 . 64 


51.43 


,58,42 


51.68 


,58,19 ,51,94 


78 


79 


59.62 


51.83 


59.40 


52.09 


59,17 


.52.35 


58,94 


52.60 


79 


80 
81 


60.38 


.52.48 


60.15 


52.75 
53.41 


,59,92 
60,67 


53.01 


59,68 


53.27 


80 


61.13 


53,14 


60.90 


53.67 


60,43 


53 . 94 


81 


82 


61.89 


.53.80 


61.65 


54.07 


61.41 


.54.33 


61,18 


.54.60 


82 


83 


62.64 


54.45 


62.40 


.54.73 


62.16 


,55,00 


61,02 


55.27 


83 


84 


63.40 


55.11 


63.15 


55.38 


62.91 


55.66 


62,67 


.55.93 


84 


85 


64.15 


55.76 


63.91 


.56.04 


63.66 


56.32 


63.41 


56 . 00 


85 


86 


64.90 


.56.42 


64.66 


56.70 


64.41 


56.99 


64.16 


57 . 27 


86 


87 


65.66 


57.08 


65.41 


57.36 


65.16 


57 . 65 


' 64.91 


.57.93 


87 


88 


66.41 


.57.73 


66.16 


58 . 02 


65.91 


58.31 


i 65 . 65 


,58 . 60 


88 


89 


67.17 


58.39 


66.91 


58.68 


66.66 


58.97 


66.40 1 59.26 


89 


90 
91 


67.92 


59.05 


67.67 


59.34 


67.41 


59.64 
60.30 


67.15 1 59.93 
67.89 60.60 


90 
91 


68.68 


.59.70 


68.42 


60.00 


68.15 


92 


69.43 1 60.36 


69.17 


60.66 


68.90 


60.96 


68.64 61.26 


92 


93 


70,19 i 61.01 


69.92 


61.32 


69,65 


61,62 


69.38 1 61.93 


93 


94 


70,94:61.67 


70.67 


61.98 


70,40 


62,29 


70.13 1 02.59 i 94 1 


95 


71.70 62.33 


71.43 


62.64 


71,15 


62.95 


70.88 ; 63.26 | 95 1 


96 


72.45 62.98 


72.18 


63.30 


71.90 


63.61 


71.62 


63.92 96 


97 


73.21 63.64 


72.93 


63.96 


72.65 


64.27 


72.37 


64.59 97 


98 


73.96 


64.29 


73,68 


64.62 


73.40 


64.94 


73.11 


65.26 I 98 


99 


74.72 


64.95 


74.43 


65,28 


74.15 


65.60 


73.86 


65.92 


99 


100 
1 

3 


75.47 


65.61 


75,18 


65.93 


74.90 


66.26 


74.61 


66.59 


100 

1 

3 


Der 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


D.p. 


Lat. 


49 Deg. 


481 Deg. 


48J Deg. 


48i Deg. 



86 



TKAVERSE TABLE. 



1 

s 
? 

1 


42 Deg. 


m Dog. 


42i Deg. 


~ 

42| Deg. 


3 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0.74 


0.67 


"oTt^ 


0.67 


0.74 


0.68 


0.73 


0,68 


r 


2 


1.49 


1..34 


1.48 


1.34 


1.47 


1.35 


1.47 


1.36 


2 


3 


2.23 


2.01 


2.22 


2.02 


2.21 


2.03 


2.20 


2.04 


3 


4 


2.97 


2.68 


2.96 


2.69 


2.95 


2.70 


2.94 


2 . 72 


4 


5 


3,72 


3.35 


3.70 


3.36 


3.69 


3.38 


3.67 


3.39 


5 


6 


4.46 


4.01 


4.44 


4.03 


4.42 


4.05 


4.41 


4.07 


6 


7 


5.20 


4.68 


5.18 


4.71 


5.16 


4.73 


5.14 


4.75 


7 


8 


5.95 


5.35 


5.92 


5.. 38 


5.90 


5.40 


5.87 


5.43 


8 


9 


6.60 


6.02 


6.66 


6.05 


6.64 


6.08 


6.61 


6.11 


9 


10 


7.43 


6.69 


7.40 


6.72 


7.37 


6.76 


7.34 

8.08" 


6.79 

7,47 


10 
11 


11 


8.17 


7.36 


8.141 7.4U 


8. 11 


7.43 


12 


8.92 


8.03 


8.88 8.07 


8.85 


8.11 


8.81 


8,15 


12 


13 


9.66 


8.70 


9.62, 8 , 74 


9.. 58 


8.78 


9.. 55 


8.82 


13 


14 


10.40 


9.37 


10.36 1 9.41 


10.32 


9.46 


10.28 


9,. 50 


14 


15 


11.15 


10.04 


11.10 10.09 


11.06 


10.13 


11.01 


10.18 


15 


16 


11.89 


10.71 


11.84! 10.76 


11.80 


10.81 


1 1 . 75 


10.86 


10 


17 


12.63 


11.38 


12.58 i 11.43 


12.. 53 


11.48 


13.48 


11. .54 


17 


18 


13.38 


12.04 


13.32 12.10 


13.27 


12.16 1 13.22 


12.22 


18 


19 


14.12 


12.71 


14.06 


12.77 


14.01 


12.84 


13.95 


12.90 


19 


20 


14.86 


13.38 


14.80 
1. 57.54 


13.45 


14.75 
15.48 


13.51 
14.19 


14.69 

1.5". 42 


13.58 


20 

21 


21 


15.61 


14.05 


14.12 


14,25 


22 


16.35 


14.72 


16.28 


14.79 


16.22 


14.86 


16.16 


14,93 


22 


23 


17.09 


15.39 


17.02 


15. 4C 


10.96 


15.54 


16.89 


15.01 


23 


24 


17.84 


16.06 


17.77 


16.14 


17.69 


16.21 


17.62: 16.29 


24 


25 


18.. 58 


16.73 


18.51 


16.81 


18.43 


16.89 


18.36; 16.97 


25 


26 


19.32 


17.40 


19.U5 


17.48 


19.17 


17.57 


19.09 ! 17.05 


26 


27 


20.06 


18.07 


19.99 


18.15 


19.91 


18.24 


19.83 


18.33 


27 


2S 


20.81 


18.74 


20.73 


18.83 


20 . 64 


18.92 


20.. 56 


19,01 


28 


29 


21.55 


19.40 


21.47 


19.. 50 


21.38 


19.59 


21.30 


19,09 


29 


30 


22.29 


20.07 


22.21 


20.17 


22.12 


20.27 


22 . 03 


20,30 


30 


31 


23.04 


20.74 


22.95 


20.84 


22 .'86 


20.94 


22.76 


21,04 


' 3r 


32 


23.78 


21.41 


23.69 


21.52 


23 . 59 


21.62 


23.. 50 


21,72 


32 


33 


24.. 52 


22.08 


24.43 


22.19 


24.. 33 


22.29 


24.23 


22,40 


33 


34 


25.27 


22 . 75 


25 . 1 7 


22.86 


25.07 


22.97 


24.97 


23.08 


34 


35 


26.01 


23.42 


25.91 


23.53 


25.80 


23.65 


25.70 


23 . 76 


35 


36 


26.75 


24.09 


26.65 


24.21 


26.-54 


24.32 


26.44 


24,44 


36 


37 


27 50 


24.76 


27.39 


24.88 


27.28 


25.00 


27.17 


25,12 


37 


38 


28.24 


25.43 


28.13 


25.. 55 


28.02 


25.07 


27.90 


25 , 79 


38 


39 


28.98 


26.10 


28.87 


26.22 


28 , 75 


26.35 


28 . 64 


26,47 


39 


40 
41 


29.73 


26.77 
27.43 


29.61 
30.35 


26.89 
27.57 


29.49 


27.02 
27.70 


29.37 


27,15 

27,83 


40 
41 


30.47 


30 . 23 


30 . 1 1 


42 


31.21 


28.10 


31.09 


28.24 


30.97 


28.37 


30.84 


28,51 


42 


43 


31.96 


28.77 


31.83 


28.91 


31.70 


29.05 


31. .58 1 29.19 


43 


44 


32.70 


29.44 


32.57 


29.58 


32.44 


29.73 


,32.31 29.87 


44 


45 


33.44 


30.11 


33.31 


30.26 


33.18 


30.40 


33.04 .30.55 


45 


46 


34.18 


30.78 


34.05 


30.93 


33.91 


31.08 


33.78 31.22 


46 


47 


34.93 


31.45 


34.79 


31.00 


34.65 


31.75 


134.51 131.90 


47 


48 


35.67 


32.12 


35 . 53 


32.27 


35.39 


32.43 


j 35 . 25 ! 32 . 58 


48 


49 


36.41 


32.79 


36.27 


32.95 


.36.13 


33.10 


,35,98 i 33.26 


49 


50 


37.16 


33.46 


37.01 
Dep. 


33.62 


36.86 


33.78 


36 . 72 


33,94 
Lat. 


_50^ 

1 


14 

5 


Dep. 


Lat. 


Lat. 


Dep. 


Lat. 


Dep, 


48 


Deg. 


471 Deg. 


47iDeg. 


m 


Deg. 



TRAVEKSE TABLE- 



87 



5 

X 


42 Deg. 


42k Deg. 


42i Deg. 


421 Deg. 



51 


3 


Lat 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


TT 


37.90 


34.13 


37.75 


34.29 


37.60 


34.46 


37.45 


34.63 


52 j 38.64 


34.79 


38.49 


34.96 


38.34 


35.13 


38.18 


35.30 


52 


53 '39.39 35.46 


39,23 


35.64 


39.08 


35.81 


38.92 


35.93 


53 


54 140.13 30.13 


39,97 


36.31 


39.81 


36,48 


39.65 


36.66 


54 


55 


40.87 


36.80 


40,71 


36.98 


40.55 


37,16 


40.39 


37.. 33 


55 


56 


41.63 


37.47 


41,45 


37.65 


41.29 


37,83 


41.12 


38.01 


56 


57 


42.36 


38,14 


42,19 


38.32 


42.02 


38.51 


41.86 


38,69 


57 


58 


43.10 


38.81 


42,93 


39.00 


42.76 


39.18 


42.69 


39,37 


58 


59 


43.85 


39.48 


43,67 


39.67 


43.50 


39.86 


43.32 


40.05 


59 


60 

-6T 


44.59 


40,15 


44,41 


40.. 34 


44.24 


40.. 54 


44.06 


40 . 73 


60 
61 


45.33 


40,82 


45.15 


41.01 


44.97 


41.21 


44.79 


41.41 


63 


46.07 


41,49 


45.89 


41.69 


45,71 


41.89 


45.53 


42.09 


62 


63 


46.82 


42,16 


46.63 


42.36 


46,45 


42.56 


46.26 


42.76 


63 


64 


47.58 


42,82 


47.37 


43.03 


47,19 


43,24 


47,00 


43.44 


■ 64 


65 


48.30 


43,49 


48.11 


43 . 70 


47,92 


43.91 


47.73 


44.12 


65 


66 


49.05 


44,16 


48.85 


44,38 


48,66 


44.. 59 


48.47 


44.80 


66 


67 


49.79 


44.83 


49.59 


45.05 


49,40 


45.26 


49.20 


45.48 


67 


68 


50.53 


45.50 


50.33 


45.72 


.50.13 


45.94 


49.93 


46.16 


68 


69 


51.28 


46,17 


51.07 


46,39 


.50.87 


46.62 


50.67 


40.84 


69 


70 
71 


52.02 


46,84 


51.82 


47,07 


51.61 


47.29 


51.40 


47.-53 
48.19 


70 
71 


52.76 


47,51 


52,56 


47,74 


52.35 


47.97 


53.14 


72 


.53.51 


48,18 


53.30 


48.41 


.53.08 


48.64 


53.87 


48.87 


73 


73 


54.25 


48,85 


.54,04 


49.08 


53.82 


49.i:'2 


153.61 


49.55 


73 


74 


54.99 


49,52 


.54,78 


49.76 


54.56 


49.99 


154.34 


.50.33 


74 


75 


.55.74 


50.18 


55.52 


50.43 


55,30 


50.67 


i 65,07 


.50.91 


75 


76 


56.48 


.50.85 


56.36 


51.10 


.56.03 


51.34 


55.81 


51.59 


76 


77 


57.22 


51.52 


57.00 


51,77 


56 , 77 


62.02 


56.. 54 


52.27 


77 


78 


57,97 


.52.19 


57.74 


53,44 


57,51 


.52.70 


.57.28 


52.95 


78 


79 58.71 


52.86 


58.48 


.53,12 


58,24 


53.37 


.58.01 


53.63 


79 


80 
81 


59.45 


.53.-53 


.59,22 


53.79 


58.98 [54.05 


i 58.75 


54,30 


80 
81 


GO. 19 


54,20 


59.96 


,54.46 


59.72 


54.72 


59.48 


54.98 


82 


60.94 


54,87 


60.70 


55.13 


60.46 


55.40 


; 60.21 


55.66 


82 


83 


61.68 


55,54 


61.44 


55.81 


61.19 


56.07 


60.95 


56.. 34 


83 


84 


62.42 


56,21 


62.18 


56.48 


61.93 


.56.75 


61.68 


67.02 


84 


85 


63.17 


56,88 


62,92 


57.15 


62.67 


57.43 


62.42 


57.70 


85 


86 


63.91 


57,. 55 


63.66 


57.82 


63,41 


58.10 


63.15 


68.38 


86 


87 


64.65 


58.21 


64,40 


.58.50 


64,14 


58.78 


,63.89 


59.06 


87 


88 


65.40 


58.88 


65,14 


59.17 


64.88 


59.45 


164.62 


59.73 


88 


89 


66.14 


59.55 


65.88 


59.84 


65.62 


60,13 


i 65.-35 


60.41 


89 


90 
91 


66.38 


60.22 


66.62 


60.51 


66.35 


60,80 


66.09 


61.09 


90 
91 


67.63 


60.89 


67.36 


61.19 


67.09 


61.48 


66.82 


61.77 


92 


68.37 


61.56 


68.10 


61.86 


67.83 


.62.15 


67,-56 


63.45 


92 


93 


69.11 


62.23 


68.84 


62.53 


68.57 


62.83 


68.29 


63.13 


93 


94 


69.86 162.90 


69.. 58 


63.20 


69.30 


63,51 


169.03 


63.8] 


94 


95 


70.60 63.57 


70.32 


63.87 


70.04 


64,18 


; 69,76 


64,49 


95 


96 


71.34 


64.24 


71.06 


64.55 


70.78 


64,86 


170.49 


65,16 


96 


97 


72.08 


64.91 


71.80 


65.22 


71.52 i 65.53 


71,23 


65.84 


97 


98 


72.83 


65.57 


72.54 


65.89 


72.25 


66.21 


71.96 


66.52 


98 


99 


73.57 


66.24 


73.28 


66,56 


72.99 


66,88 


72.70 


67.20 


99 


100 

s 


74.31 


66.91 


74.02 


67.24 


73.73 


67,56 


73.43 


67,88 


100 


Dep, 


Lat, 


Dep. 


Lat. 


Dep, 


Lat. 


Dep, 


Lat, 


8 

V. 

p 


48 Deg. 


471 Deg. 


47i Deg. 


47i Deg. 



TRAVERSE TA.ELE. 



1 


43 Deg. 


43i Deg. 


43i Deg. 


431 Deg. 


1 
a 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


0,73 


0.68 


0.73 


0.69 


0.73 


0.69 


0.72 


0.69 


2 


1.46 


1.36 


1.46 


1.37 


1.45 


1.38 


1.44 


1.38 


2 


3 


2.19 


2.05 


2.19 


2.06 


2.18 


2.07 


2.17 


2.07 


3 


4 


2.93 


2.73 


2.91 


2.74 


2.90 


2.75 


2.89 


2,77 


4 


5 


3.66 


3.41 


3.64 


3.43 


3.63 


3.44 


3.61 


3.46 


5 


6 


4.39 


4.09 


4.37 


4.11 


4.35 


4.13 


4.33 


4.15 


6 




5.12 


4.77 


5.10 


4.80 


5.08 


4.82 


5.06 


4.84 


7 


8 


5.85 


5.46 


5.83 


5.48 


5.80 


5.51 


5.78 


5.53 


8 


9 


6.58 


6.14 


6.56 


6.17 


6.. 53 


6.20 


6.50 


6.22 


9 


10 


7.31 


6.82 


7.28 


6.85 


7.25 


6.88 


7.22 


6 92 


10 


11 


8.04 


7.50 


8.01 


7.54 


7.98 


7.57 


7.95 


7.61 


11 


12 


8.78 


8.18 


8.74 


8.22 


8.70 


8.26 


8.67 


8.30 


12 


13 


9.51 


8.87 


9.47 


8.91 


9.43 


8.95 


9.39 


8.99 


13 


14 


10.24 


9.55 


10.20 


9.59 


10.16 


9.64 


10.11 


9.68 


14 


15 


10.97 


10.23 


10.93 


10.28 


10.88 


10.33 


10.84 


10.37 


15 


16 


1 1 , 70 


10.91 


11.65 


10.96 


11.61 


11.01 


11.56 


11.06 


16 


17 


12.43 


11.59 


12.33 


11.65 


12.33 


11.70 


12.28 


11.76 


17 


18 


13.16 


12.28 


13.11 


12.33 


13.06 


12.39 


13.00 


12.45 


18 


19 


13.90 


12.96 


13.84 


13.02 


13.78 


13.08 


13.72 


13.14 


19 


20 

21 


14.63 


13.64 


14.57 


13.70 


14.51 


13.77 


14.45 


13.83 


20 


15.36 


14.32 


"15^30 


14.39 


15.23 


14.46 


15.17 


14.52 


21 


22 


16.09 


15.00 


13.02 


15.07 


15.96 


15.14 


15.89 


15.21 


22 


23 


16.82 


15.69 


16.75 


15.76 


16.68 


15.83 


16.61 


15.90 


23 


24 


17.55 


16.37 


17.48 


16.44 


17.41 


16.52 


17.34 


16.60 


24 


25 


18.28 


17.05 


18.21 


17.13 


18.13 


17.21 


18.06 


17.29 


25 


26 


19.02 


17.73 


18.94 


17.81 


18.86 


17.90 


18.78 


\7.9a 


26 


27 


19.75 


18.41 


19.67 


18 50 


19.59 


18.59 


19.50 


18.67 


27 


28 


20.48 


19.10 


20.39 


19.19 


20.31 


19.27 


20.23 


19.36 


28 


29 


21.21 


19.78 


21.12 


19.87 


21.04 


19.96 


20.95 


20.05 


29 


30 
'31 


21.94 


20.46 


21.85 


20.56 


21.76 


20.65 


21.67 


20.75 


30 


22.67 


21.14 


22.58 


21.24 


22.49 


21.34 


22.39 


21.44 


31 


32 ' 23.40 


21.82 


23.31 


21.93 


23.21 


22.03 


23.12 


22.13 


32 


33 


24.13 


22.51 


24.04 


22.61 


23.94 


22.72 


23.84 


22.82 


33 


34 


24.87 


23.19 


24.76 


23.30 


24.66 


23.40 


24.56 


23.51 


34 


35 


25 . 60 


23.87 


25.49 


23.98 


25 . 39 


24.09 


25.28 


24.20 


35 


36 


•^6.. 33 


24.55 


26.22 


24.67 


26.11 


24.78 


26.01 


24.89 


36 


37 


27.06 


25.23 


26.95 


25.35 


26.84 


25.47 


26.73 


25.59 


37 


38 


27.79 


25.92 


27.68 


26.04 


27.56 


26.16 


27.45 


26 . 28 


38 


39 


28.. 52 


26.60 


28.41 


26.72 


28.29 


26.85 


28.17 


26.97 


39 


40 
41 


29.25 27.28 


29.13 
29.86 


27.41 


29.01 


27.53 


28.89 


27.66 


40 
'41 


29.99 27.96 


28.09 


29.74 


28.22 


29.62 


28.35 


42 


.30.72 


28.64 


30 . 59 


28.78 


30.47 


28.91 


30.34 


29.04 


42 


43 


31.45 


29.33 


31.32 


29.46 


31.19 


29.60 


31.06 


29.74 


43 


44 


32.18 


30.01 


32.05 


30.15 


31.92 


30.29 


31.78 


30.43, 44 


45 


32.91 


30.69 


32.78 


30.83 


32.64 


30.98 


.32.51 


31.12 ! 45 


46 


.33.64 


31.37 


33.51 


31.52 


33.37 


31.66 


33.23 


31.81 46 


47 


34.37 


32.05 


34.23 


32.20 


34.09 


32.. 35 


33.95 


32.50 47 


48 


35.10 


32.74 


34.96 


.32.89 


34.82 


33.04 


34.67 


33.19 48 


49 


35.84 


33.42 


35.69 


33.57 


35.. 54 


33,73 


35.40 


.33.88 49 


50 


36.. 57 


34.10 


36.42 


34.26 


36.27 


34.42 


36.12 


34.. 58 50 


1 
.2 
Q 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


5 


47 Deg. 


46| Deg. 


46i Deg. 


46\ Deg. 



TRAVERSE TABLE. 



89 



p 

~5l 


43 Deg. 


43i Deg. 


43i Deg. 


433 Deg. 


1 
51 


Lat. 


Dep. 


Lat. 1 Dep. 


Lat. 


Dep. 


Lat. 

36.84 


Dep. 


37.30 


34.78 


37.15 34.94 


36.99 


35.11 


35.27 


52 


38.03 


35.46 


37.88 


35.63 


37.72 


35.79 


37.56 


35 . 96 


52 


53 


38.76 


36.15 


38.60 


36.31 


38.44 


36.48 


38.29 


36.65 


53 


5i 


39.49 


36.83 


39.33 


37.00 


39.17 


37.17 


39.01 


37.. 34 


54 


55 


40.22 


37.51 


40.06 


37.69 


.39.90 


37.86 


39.73 


38.03 


55 


56 


40.96 


38.19 


40.79 


38.37 


40.62 


38.55 


40.45 


.38.72 


56 


57 


41.69 


38.87 


41.. 02 


39.06 


41.35 


39.24 


41.17 


39.42 


67 


58 


42.42 


39.. 56 


42.25 


39.74 


42.07 


39.92 


41.90 


40.11 


58 


59 


43.15 


40.24 


42.97 


40.43 


42.80 


40.61 


42.62 


40.80 


59 


60 
61 


43.88 
44.61 


40.92 


43.70 


41.11 


43.52 
44.25 


41.30 
41.99 


43.34 


41.49 


60 
61 


41.60 


44.43 


41.80 


44.06 


42.18 


62 


45.34 


42.28 


45 . J 6 


42.48 


44.97 


42 . 68 


44.79 


42.87 


62 


63 


46.08 


42.97 


45.89 143.17 | 


45 . 70 


43.37 


45,51 


4 3.. 57 


63 


64 


46.81 


43.65 


46.62 


43.85 


46.42 


44.05 


46.23 


44.26 


64 


65 


47.54 


44.33 


47.34 


44.. 54 


47.15 


44.74 


46.95 


44.95 


65 


G6 


48.27 


45.01 


43.07 


45 . 22 


47.87 


45.43 


47.68 


45.64 


66 


67 


49.00 


45.69 


48.80 


45.91 


48.60 


46.12 1 


48.40 


46.33 


67 


68 


49 . 73 


46.38 


49.53 


4 6.. 59 


49.33 


46.81 


49.12 


47.02 


68 


69 


50.46 


47.06 


.50.26 


47.28 


.50 . 05 


47.50 


49.84 


47.71 


69 


70 
71 


51.19 
51.93 


47.74 

48.42 


.50.99 


47.96 
"48.65 


.50.78 


48.18 


50.57 
51.29 


48.41 


70 
71 


51.71 


51.50 


48.87 


49.10 


72 


.52 . 66 


49.10 


52.44 


49.33 


52.23 


49.56 


52.01 


49.79 


72 


73 


53.39 


49.79 


53.17 '50.02 


.52.95 


.50.25 


52 . 73 


50.48 


73 


74 


.54.12 


.50.47 


53.90 


.50.70 


53.68 


50.94 


.53.45 


51.17 


74 


75 


54.85 


51.15 


54.63 


51.39 


54.40 


51.63 


54.18 


51.86 


75 


76 


55.58 


51.83 


55.36 


52 . 07 


55.13 


.52.31 


.54.90 


52.55 


76 


77 


56.31 


52.51 


56.08 


52.76 


55.85 


53.00 


55.62 


53 . 25 


77 


78 


57.05 


53.20 


56.81 


53,44 


56.58 


53 . 69 


56.34 


53 . 94 


78 


79 


57.78 


53.88 


57.. 54 


54.13 


57.30 


54.38 


57.07 


54.63 


79 


80 
81 


58.51 


54 . 56 


58.27 


.54.81 


.58.03 
.58.70 


.55.07 
55 . 76 


57.79 
.58.51 


.55.32 
56.01 


80 
81 


59.24 


55.24 


59.00 


55.. 50 


82 


59.97 


55 . 92 


59.73 


56.18 


59.48 


56.45 


59.23 


56.70 


82 


83 


60 . 70 


56.61 


60.45 


50.87 


60.21 


,57.13 


,59.96 


57.40 


83 


8-i 


61.43 


57.29 


61.18 


57.56 


60.93 


57.82 


60.68 


58.09 


84 


85 


62.17 


57.97 


01.91 


58.24 


61.66 


.58.51 


61.40 


58 . 7.S 


85 


86 


62.90 


.58.65 


62.64 


58.93 


62.38 


59.20 


! 62.12 


59.47 


86 


87 


63.63 


59.33 


63.37 


59.61 


63.11 


,59.89 


1 62.85 


60.16 


87 


88 


64.36 


60.02 


64.10 


60 . 30 


63.83 


60 . .58 


63.. 57 


60.85 


88 


89 


65.09 


60.70 


64.82 


60.98 


64.56 


61.26 


64.29 


61. .54 


89 


90 
91 


65.82 


01.38 


65.55 


61.67 


65.28 


61.95 


1 65.01 


62.24 


90 
91 


66 . 55 


62.06 


'66.28 


62.35 


66.01 162.64 


65.74 


62.93 


92 


67.28 162.74 


67.01 


63.04 


66.73 63.33 


66.46 63.62 


92 


93 


68.02 63.43 


67.74 


63.72 


67.46 64.02 


j 67.18 1 64.31 


93 


94 


68.75 64.11 


68.47 


64.41 


68.19 64.71 


167.90 


65.00 


94 


95 


69.48 64.79 


69.20 


65.09 


168.91 


65.39 


•68.62 


65 . 69 


95 


96 


70.21 , 65.47 


69.92 


65.78 


69 . 64 


66.08 


1 69 . 35 


66.. 39 


96 


97 


70.94 66.15 


70.65 


66.46 


70.36 


66.77 


70.07 


67.08 


97 


98 


71.67 


66.84 


71.37 


67.15 


71.09 


67.46 


70.79 


67.77 


98 


99 


72.40 


67.52 


72.11 


67.83 


71.81 


68.15 


71.51 


68.46 


99 


100 

1 
1 

3 


73.14 


68.20 


72.84 


68.52 


72.54 


08.84 


72.24 


69.15 


100 

1 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


47 Deg. 


46} Deg. 

1 


46i Deg. 


46J Deg. 



90 



TRAVERSE TABLE. 



g 

? 

1 


44 Deg. 


444 Deg. 


44i Deg. 


44J Deg. 


45 Deg. 


p 

3 


Lat. 


Dep. 


Lat. 


Dep. 


Lat. 
0.71 


Dep. 

"oTto 


Lat. 


Dep. 

"o?n 


Lat. 


Dep. 


0.72 


0.69 


0.72 


0.70 


0.71 


0.71 


0.71 


I 


2 


1.44 


1.39 


1.43 


1.40 


1.43 


1.40 


1,42 


1.41 


1.41 


1.41 




3 


2.16 


2.08 


2.15 


2.09 


2.14 


2.10 


2.13 


2.111 


2.12 


2.12 


3 


4 


2.88 


2.78 


2.87 


2.79 


2.85 


2.80 


2.84 


2.821 


2.83 


2.83 


4 


5 


3.60 


3.47 


3.. 58 


3.49 


3.5V 


3.50 


3.55 


3.. 52 


3.54 


3.. 54 


5 


6i 4.32 


4.17 


4.30 


4.19 


4.28 


4.21 


4.26 


4.22! 


4.24 


4.24 


fi 


7 


5.04 


4.86 


5.01 


4.88 


4.99 


4.91 


4.97 


4.93i 


4.95 


4.95 




8 


5.75 


5.56 


5.73 


5., 58 


5.71 


5.61 


5.68 


5.63, 


5.66 


5.66 


8 


9 


6.47 


6.25 


6.45 


6.28 


6.42 


6.31 


6.39 


6.. 34 


6.36 


6 . 36 


9 


10 
11 


7.19 


6.95 
7.64 


7.16 

7. '88 


6.98 


7.13 


7.01 
7.71 


7.10 


7.04 
7.74! 


7.07 


7.07 

7.78 


10 


7.91 


7.68 


7.85 


7.81 


7.78 


12 


8.63 


8.34 


8.60 


8.37 


8.56 


8.41 


8.52 


8.45i 


8.49 


8.49 


12 


13 


9.35 


9.03 


9.31 


9.07 


9.27 


9.11 


9.23 


9.I5I 


9.19 


9.19 


13 


14 


10.07 


9.73 


10.03 


9.77 


9.99 


9.81 


9.94 


9.86! 


9.90 


9.90 14 


15 


10.79 


10.42 


10.74 


10.47 


10.70 


10.51 


10.65 


10.561 10.61 


10.61 15 


16 


11.51 


11.11 


11.46111.16 
12.18 11 .86 


11.41 


11.21 


11.36 


11.26! 11.31 


11.31 16 


17!l2.23 


11.81 


12.13 


11.92 


12.07 


11.971 


12.02 


12.02 17 


18 


12.95 


12.50 


12.89 


12.56 


12.84 


12.62 


12.78 


12.671 


12.73 


12.73 18 


19 


13.67 


13.20 


13.61 


13.26 


13.. 55 


13.32 


13.49 


13.381 


13.43 


13.43 19 


20 

21 


14.39 
15.11 


13.89 
14.59 


14.33 


13.96 
14765 


14.26 


14.02 


14.20 


14.081 


14.14 
14.8.5 


14.14120 

14.85:21 


15.04 


14.98 


14 72 


14.91 


14.78i 


22 


15.83 


15.28 


15.76 


15.35 


15.69 


15.421' 15. 62 


15.49 


15.56 


15.56|22 


23 


16.54 


15.98 


16.47 


16.05 


16.40 


16.12.116.33 


16.19 


16.26 


16.2623 


24 


17.26 


16.67 


17.19 


16.75jll7.12 


16.82 '17.04 


16.90 


16.97 


16.97 24 


25117.98 


17.37 


17.91 


17.44 


17.83 


17.52 17.75 


17.60 


17.68 


17.83125 


26|I8.70 


18.06 


18.62 


18.14 


18.54 


18.22| 18.46 


18.30 


18.38 


18.38126 


27119.42 


18.76 


19.34 


18.84 


19.26 


18.92 19.17 


19.01 


19.09 


19.09127 


28 20.14 


19.45 


20.06 


19.54 


19.97 


19.63 19.89 


19.71 


19.80 


19.80128 


29|20.8fi 


20.15 


20.77 


20.24 


20.68 


20.33 20.60 


20.42 


20.51 


2O.51I29 


30 121.. 58 
31122.30 
32 23.02 


20.84 


21.49 


20 . 93 


21.40 
22.11 


21 .03 21.31 
21.73 22.02 


21.12 


21.21 


21.21 30 
21.92 31 


21.53 


22.21 


21.63 


21.82121.92 


22.23 


22.92 


22.33 


22.82 


22.43,22.73 


22.53 


22.63 


22.63 32 


33 23.74 


22.92 


23.64 


23.03 


23.54 


23.13 23.44 


23.23 


23.33 


23., 33! 33 


34124.46 


23.62 


24.35 


23.72 


24.25 


23.83:24.15 


23.94 


24.04 


24.04134 


35 


25.18 


24.31 


25.07 


24.42 


24.96 


24.53,24.86 


24.64 


24.76 


24.75135 


36 


25.90 


25.01 


25.79 


25.12 


25.68 


25. 23 1 25.67 


25.34 


25.46 


25.46!.36 


37 


26.62 


25.70 


26.50 


25.82 


26.39 


25.93:26.28 


26.05 


26.16 


26.16 


37 


38 


27.33 


26.40 


27.22 


26.. 52 


27.10 


26.63126.99 


26 . 75 


26.87 


26.87 


38 


39 


28 . 0.1 


27.09 


27.94 


27.21 


27.82 


27.341 27.70 


27.46 


27.58 


27.58 


39 


40 
41 


28.77 
29.49 


27.79 


28.65 


27.91 


28.53 


28.04 28.41 
28.74 29.12 


28.16 


28.28 


28 . 28 
28.99 


40 
41 


28.48 


29.37 


28.61 


29.24 


28.86 


28.99 


43 


SO. 21 


29.18 


30.08 


29.31 


29.96 


29.44 29.83 


29.57 


29.70 


29.70 


42 


43 


30.93 


29.87 


30.80 


30.00 


30.67 


30.14 30. .54 


30.27 


30.41 


30.41 


43 


44 


31.65 


30.56 


31.52 


30.70 


31.38 


30.84 31.25 


30.98 


31.11 


31.11 


J.4 


45 


32.37 


31.26 


32.23 


31.40 


32.10 


31.54131.96 


31.68 


31.82 


31,82 


45 


46 


33.09 


31.95 


32.95 


32.10 


32.81 


32.24 32.67 


32.38 


32.53 


32.53 


46 


47 


33.81 


32.65 


33.67 


32.80 


33.52 


32.94133.38 


33.09 


33.23 


33.23!47 


48 


34.. 53 


33.34 


34.38 


.33.49 


34.24 


33.64 34.09 


33.79 


.33.94 


33.94148 


49 


35 . 25 


34.04 


3.0.10 


34.19 


34.95 


.34.341 34.80 


34.50 


34.65 


34.65149 


50'35.97 


34.73 


35.82 


34.89 


35.66 


35.05^35.61 
Let, 1 Dep. 


35.20 
Lat. 


35.36 
Dep. 


3^3^ 
Lat. 


50 

1 

s 


1 
.2 

q 


Dcp. 


Lat. 


Dep. 1 Lat. 


Dep. 


46 Deg. 


451 Deg. 


45h Deg. 


451 Deg. 


45 Deg. 



travt:rse tablr. 



91 



5' 41 Deg. 44i D.g. 

1 1 1 


44i Deg. 


441 Deg. 


45 Deg. 



1 


g ' Lai. j Dep. Lat. ' Dep. 
51 36.69 3.-). 13 36.. 53 3.5.591 


Lat. Dep. 


Lat.| 


Dep. 


Lat. , Dep. g 


36.38 35.75 136.22 35.90 36.06 36.06 51 | 


5-i37.-ir36.13 37.25:36.29 


37.09 36.451 


36.93 36.61 36. 77136. 77 52 


53,35.12 36.32 37.93 36. 9Si 


37.80 37.15! 


37.64137.3137.48 37.48 S3 


5413^.84 37.51 38. 6S 37.68; 


38.52 


37.85 


38.35 33.02 38.18l3S.18l 54 


5.5I39. 56 33,21 39. 4U 38.3S!;39.23 


38.55 


39.06 38.72 38.89|38.89! 55 


5(;;40.23 3S.90 40.11 39.08 139.94 


39.25 


39.77:39.42 39.60 


39.60 56^ 


57:41.00^39.60 40.83:39.77;j40.66 


39.95 


40.48:40.13 40.31 


40.31! 57 


5341.72 40.29 41 .55.40. 47| 41 .37 


40.65 


41.19 40.83 41.01 


41.0li 58 


59-42.44l40.9S, 42. S6!41. 17 42.08 


41 . 35 


41. 90141. .54 41.72 


41.72 59 


60 43. 1 6:41 .6S 42.93j41 .871142.79 


42.05 


42.61 42. 24 42.43142. 431 60 


fi i 143 . s'N'42 .37,43. 69 42 . 57!i43 5i 


42.76 


43.32142.94 43.13143.13! 61 


6244.61(43.07' 44.41143.26 !44 22 


43.46 


44. 03143. 66 43.84 43.84 62 


634.5.32 43.76 45. 13143. 96!;44 03 


44.16 


44.74:44.3.5 44.55:44.55, 63 


64 46.0-1 44. 46!;45. 84144. 66ii45. 65 


44.86 


45. 45!45. 06 ,45.25:45.251 64 


65146.76 45.15 46. 56|45. 36:46 36 


45.56 


46.16145.76145.96145.961 65 


66147.48 45. S5: 47. 28146. 051147. 07 


46.26 


46. 87!46.46'46. 67146. 671 66 


67 43.20 46.54 47.99|16.75;:47.79 


46.96|47.58;47.17:47.38i47.38| 671 


68 43.92 47.24 48. 7 1147. 45 48.. 50 


47. 661148. 29l47.87:;48. 08:48. 081 38 | 


69 49 . 63 47 . 93 49 .42i43 . 15,49 . 2 1 


48. 36i;49.00;4S. 58 ,48.79:48.79 
49.06:149.71 49.28, :49. 50, 49. 50 


69 


7U 5J.35 43.63! 50. 14 43.85' 49.93 


70 


7 h5 1 . 07 49 . 32 50 . 86j49 . 54, 50 . 64 


49.76:50.42:49.98 50.20150.20 


71 


72 :5 1 . 79 50 .02 5 1 . 571 50 . 24 5 1 . 35 


50. 47!:51.13!50. 69 150.91150. 91 


72 


73 ;.52 .51 50 . 7 1 ' 52 . 29150 . 94^ 52 . 07 


51.17i:5l.84'51.39 


51.62l51.62i 73 


74 53.23 51.40 53.01151.64! 


52.78 


5 1.87 •.52.. 55 52.10 


52.33 52.33; 74 


7.5.53.95 52.10,153.72152.33' 


53.49 


.52.571.53.26:52.80 


.53.03.53.03' 75 


76:54.67 52. 79i:54. 44153. 031 


.54.21 


53.27:53.9753.51 


53.7453.741 76 


77|.55.39.53.49!'55.16 


53 . 73; 


54.92 


53.97 54.63 54.21 


54.45.54.45: 77 


78156.11 .54. 131155.87 


.54.43: 


55.63 


.54.67 55.39 .54.91 


55.15:55.151 78 


79!56.33 54.83|:56.59 


55.13,156.35 


55.37 56. 10 55. 63;:55. 86 55. sol 79 


S0J57.55 55.57!|.57.30 

8l'.53.27 56.27j]58.02 


55.82! 57.06 


56.07 56. 8156. 32 .56.57 56.57: SO 
56.77 57.52 57.03 .57.23 57.28! 81 


56.52! 


57.77 


82153.99 56.96158.74 


57.22! 


.58.49 


57.47,58.24 57.73 57.98 57.98 


82 


83;59.71 57.66:59.45 


57.92! 


59.20 


58.18 58.95 58.43 58.6958.69 


83 


84!60.42 58.351,60. 17 


.58.61 


59.91 


58 . 88 59 . 66 59 . 14' .59 . 40 59 . 40 


84 


85161. 14 59.05 60.89 


59.31 


60.63 


59.58,60.37 59.84 60.10 60.10 


85 


86!61.S6 5).74:61.60 


60.01 


61.34 


60.28 61.08 60.55 60.81 60.81 


86 


S7J62.58 60.44 62.32 


60.71 


62.05 


60.98 61.7961.25 61. .5261. 52 


87 


83|63.30 61.13,63.03 


61.41 


62.77 


61.68 62.50 61.95 62.23 62.23 


88 


89:64.02 61.82163.75 


62.10 


63.48 


62.33163.2162.66 62.93 62.93] 89 


9^' 64.74 62. .52:64. 47 


62.80 


64.19 


63. 08J.63. 92163.36 63.6463.641 90 


9l|65.46 63.211:65.18 


63.50 


64.91 


63.78 64.63 64. 07 '64. 35164. 351 91 


92166. 18 63.91! 65.90 


64.20jl65.62 


64.48165.34 64.77 65.05 65.05 92 


93:66.90 64.60,66.62 


64.89ii66.33 


65. 13! 66.05 65.47 65.7665.76 93 


94|67.62 65.30!:67.33 


65.59 


67.05 


65.89|66.76!66.18 66.47l66.47 94 


95[68. 34 65.991,68.05 


66.29 


67.76 


66. 59, ,67. 4 7, 66. 88 67.18 67.18 95 


96:69. r6 66.69' 68.76 


66.99 


68.47 


67.29 68.18 67.59 67.88 67.88! 9^ 


97:69.73 67.3S:69.43167.69 


69.19 


67.99 68.39 bS. 29 68.59 68.591 97 


9=^:70.50 68.03:70.20,68.33 


69.90 


68.69 69.60 68.99 69.30 69.301 98 


99i71.21 68.77! 70.91 169.08 


70.61 


69. 39!!70. 31, 69. 70 70.00 70.00' 99 


100J71. 93 69.47 
t ' Dep. ' Lat. 


j71. 63 69.78 


71.33 


70.09'171.02;70.40 


,70.71 70.711100 


Dep. : Lat. 


Dep. 


Lat. 


Dep. 


Lat. 


Dep. Lat. g 


1 46 Deg. 


45| Deg. 

i 


45 i Deg. 


!«» 


Deg. 


45 


Deg. 


1 
1. 



92 



A TABLE OF RHUMBS. 



THE DEGREES, MINUTES, AND SECONDS, THAT EVERY POINT AND QUARTER 

POhN'T OF THE COMPASS MAKES WITH 

THE MERIDIAN. 



N byE. 



N.N.E. 



N.E.byN. 



N.E. 



N.E.byE. 



E.N.E. 



E. by N. 



East. 



ITH, |PtS. 


qr. 






1 


1 







3 


N. by W. 


1 







1 


1 




1 
1 


2 
3 


N.N.W. 


2 







2 


1 




2 


2 




2 


3 


N.W. by N. 


3 







3 


1 




3 


2 




3 


3 


N.W. 


4 







4 


1 




4 


2 




4 


3 


N.W.byW. 


5 







6 


1 




5 


2 




5 


3 


W.N W. 


6 







6 


1 




6 


2 




6 


3 


W. by N. 


7 







7 


1 




7 


2 




7 


3 


West. 


8 






n 


^ 


jf 


|PU 


. qr. 


2 


48 


45 





1 


5 


37 


30 





2 


8 


26 


15 





3 


11 


15 





1 





14 


3 


45 


1 


1 


16 


52 


30 


1 


2 


]9 


41 


15 


1 


3 


22 


30 





2 





2J 


18 


45 


2 


1 


28 


7 


30 


2 


2 


30 


53 


15 


2 


3 


33 


45 





3 





3j 


33 


45 


3 


1 


39 


22 


30 


3 


2 


42 


11 


15 


3 


3 


4.5 








4 





47 


48 


45 


4 


1 


,50 


37 


30 


4 


2 


53 


26 


15 


4 


3 


56 


15 





5 





59 


3 


45 


5 


1 


61 


52 


30 


5 


2 


64 


41 


15 


5 


3 


67 


30 





6 





70 


18 


45 


6 


1 


73 


7 


30 


6 


2 


75 


56 


15 


6 


A 


78 


45 





7 





81 


33 


45 


7 


1 


84 


22 


30 


7 


2 


87 


11 


15 


7 


3 


90 








8 


U 



SOUTH. 

i 



S. by E. 



S.S.E. 



S.E. by S. 



S.E. 



S.E. byE. 



E.S.E. 



E. by S. 



East. 



S. byW. 



S.S.W. 



S.W. by S 



S.W. 



S.W. by W 



W S.W. 



W. by S. 



West 



WORKMAN S TABLE, FOR CORRECTING THE MIDDLE LATITUDE. 



93 



Mid. 


j 


















l.at. 


30 


40 


50 


60 


70 


80 


90 


100 


110 


o 


o '' 


' 


/ 


' 


/ 


/ 


/ 





/ 


15 


02 


03 


04 


06 


09 


\l 


15 


19 


23 


16 


02 


03 


04 


OG 


09 


12 


15 


18 


22 


17 


02 


03 


04 


06 


08 


11 


14 


17 


21 


IS 


02 


03 


04 


06 


08 


11 


14 


17 


20 


19 


02 


03 


04 


06 


07 


10 


13 


16 


19 


2) 


02 


03 


14 


06 


07 


09 


12 


15 


18 


21 


02 


03 


C4 


06 


07 


09 


12 


15 


18 


22 


t2 


03 


04 


06 


07 


09 


12 


15 


17 


23 


C2 


03 


04 


06 


07 


09 


12 


15 


17 


24 


02 


03 


04 


06 


07 


09 


11 


14 


10 


25 


02 


03 


04 


05 


07 


09 


11 


14 


16 


26 


02 


03 


04 


05 


07 


09 


11 


14 


16 


27 


02 


03 


04 


05 


07 


08 


11 


14 


16 


28 


02 


03 


04 


05 


06 


08 


10 


13 


15 


29 


02 


03 


04 


05 


06 


08 


10 


13 


15 


30 


02 


03 


04 


05 


06 


08 


10 


13 


15 


31 


02 


03 


04 


05 


06 


08 


10 


13 


15 


32 


02 


03 


04 


05 


06 


08 


10 


13 


15 


33 


02 


03 


04 


05 


06 


08 


10 


13 


15 


34 


02 


03 


04 


05 


06 


08 


10 


13 


15 


35 


02 


03 


04 


05 


06 


08 


10 


13 


15 


36 


02 


03 


04 


05 


06 


08 


10 


13 


15 


37 


<2 


03 


04 


05 


06 


08 


10 


13 


15 


38 


02 


03 


G4 


05 


06 


08 


10 


13 


15 


39 


02 


03 


04 


05 


06 


08 


10 


13 


15 


40 


02 


03 


04 


05 


06 


08 


10 


13 


15 


41 


02 


03 


04 


05 


06 


08 


10 


13 


15 


42 


02 


03 


04 


05 


06 


08 


10 


13 


15 


43 


02 


03 


04 


05 


07 


09 


11 


14 


16 


44 


02 


03 


04 


05 


07 


09 


11 


14 


16 


45 


02 


03 


04 


05 


07 


09 


11 


14 


16 


46 


02 


03 


04 


05 


07 


09 


11 


14 


16 


47 


02 


03 


04 


05 


07 


09 


11 


14 


16 


48 


02 


03 


04 


05 


07 


09 


11 


14 


16 


49 


02 


03 


04 


05 


07 


09 


11 


14 


17 


50 


02 


03 


04 


05 


07 


09 


11 


14 


17 


51 


02 


03 


04 


05 


07 


09 


11 


14 


17 


52 


02 


03 


04 


05 


07 


09 


12 


15 


18 


53 


02 


03 


04 


06 


07 


09 


12 


15 


18 


54 


02 


03 


04 


06 


08 


10 


13 


16 


19 


55 


02 


03 


04 


06 


08 


10 


13 


16 


19 


56 


02 


03 


04 


06 


08 


10 


13 


16 


20 


57 


02 


03 


04 


06 


08 


11 


14 


17 


20 


58 


02 


03 


04 


06 


09 


11 


14 


17 


21 


59 


02 


03 


04 


06 


09 


12 


15 


18 


22 


60 


02 


03 


04 


06 


09 


12 


15 


19 


23 


61 


02 


03 


05 


07 


09 


12 


15 


19 


23 


62 


02 


03 


05 


07 


09 


12 


16 


20 


24 


63 


02 


04 


05 


07 


09 


13 


16 


20 


24 


64 


02 


04 


06 


08 


09 


13 


17 


21 


25 


65 


02 


04 


06 


08 


10 


13 


17 


21 


25 


66 


02 


04 


06 


08 


10 


14 


18 


22 


20 


67 


02 


04 


06 


08 


11 


15 


18 


23 


27 


68 


02 


04 


06 


08 


11 


15 


19 


24 


28 


69 


02 


05 


06 


09 


12 


16 


20 


25 


30 


70 


03 


05 


06 


09 


13 


17 


21 


26 


31 


71 


04 


06 


07 


09 


13 


18 


22 


27 


33 


72 


04 


06 


08 


10 


14 


19 


23 


29 


35 



25 



94 WOUKMAN'S TABLE, FOR CORRECTING THE MIDDLE LATITUDE. 



Mid" 






















Lat. 


120 


130 


1 140 


150 


160 


170 


180 


190 


1 200 




o 


O / 


o / 


O / 


O / 


O / 


O / 


o / 


/ 


/ 




15 


27 


31 


35 


40 


45 


51 


58 


1 06 


I 14 




16 


26 


30 


34 


38 


43 


49 


56 


1 03 


1 11 




17 


25 


28 


32 


37 


42 


48 


54 


1 01 


1 08 




18 


24 


27 


31 


36 


41 


i 46 


52 


58 


1 06 




19 


23 


26 


30 


34 


40 


1 45 


50 


56 


1 03 




20 


22 


25 


29 


33 


38 


i 43 


48 


54 


1 00 




21 


21 


25 


29 


33 


37 


{ 42 


47 


53 


58 




22 


20 


24 


23 


32 


36 


! 41 


46 


51 


56 




23 


20 


24 


28 


32 


36 


40 


45 


50 


55 




24 


19 


23 


27 


31 


35 


39 


44 


48 


53 




25 


19 


23 


27 


31 


35 


39 


43 


47 


52 




26 


19 


22 


26 


30 


34 


38 


42 


47 


52 




27 


19 


22 


26 


30 


33 


38 


42 


46 


51 




28 


18 


21 


25 


29 


33 


37 


41 


46 


51 




29 


18 


21 


25 


29 


32 


36 


41 


45 


50 




30 


18 


21 


25 


28 


32 


36 


41 


45 


50 




31 


18 


21 


25 


28 


32 


36 


41 


45 


50 




32 


18 


21 


25 


28 


31 


36 


41 


45 


50 




33 


18 


21 


24 


27 


31 


35 


40 


44 


49 




34 


18 


21 


24 


27 


31 


35 


40 


44 


49 




35 


18 


21 


24 


27 


31 


35 


40 


44 


49 




36 


18 


21 


24 


27 


31 


35 


40 


44 


49 


37 


18 


21 


24 


27 


31 


35 


40 


44 


49 




38 


18 


21 


24 


27 


31 


36 


40 


45 


50 




39 


18 


21 


25 


28 


32 


36 


41 


45 


50 




40 


18 


22 


25 


28 


32 


36 


41 


45 


50 




41 


18 


22 


25 


28 


32 


37 


41 


45 


50 




43 


18 


22 


26 


29 


33 


37 


42 


46 


51 




43 


19 


23 


26 


30 


34 


38 


42 


46 


51 




44 


19 


23 


27 


30 


34 


38 


43 


47 


52 




45 


19 


23 


27 


31 


35 


39 


43 


47 


52 




46 


19 


23 


27 


31 


35 


39 


44 


48 


53 




47 


20 


23 


27 


31 


35 


40 


44 


49 


54 




48 


20 


23 


27 


31 


35 


40 


45 


50 


55 




49 


21 


24 


28 


32 


36 


41 


45 


51 


57 




50 


21 


24 


28 


32 


36 


41 


46 


52 


58 




51 


21 


24 


28 


32 


37 


42 


47 


53 


59 




52 


22 


25 


29 


33 


37 


42 


48 


54 


1 00 




53 


22 


25 


29 


33 


38 


43 


49 


55 


1 01 




54 


23 


26 


30 


34 


39 


44 


50 


56 


1 02 




55 


23 


26 


30 


35 


40 


45 


51 


57 


1 03 




56 


24 


27 


31 


3(> 


41 


46 


52 


58 


1 04 




57 


24 


28 


32 


37 


42 


48 


U 54 


1 00 


1 oe 




58 


25 


29 


33 


38 


44 


50 


55 


1 02 


1 08 




59 


26 


30 


34 


39 


45 


51 


57 


1 04 


1 IC 




60 


27 


31 


35 


40 


46 


52 


59 


1 06 


1 13 




61 


27 


31 


36 


41 


47 


54 


1 01 


1 08 


1 15 




62 


28 


32 


37 


42 


49 


56 


1 03 


1 10 


1 18 




63 


29 


33 


39 


44 


51 


58 


1 05 


1 12 


1 21 




64 


29 


34 


40 


46 


53 


1 00 


1 07 


1 14 


1 24 




05 


30 


35 


41 


48 


55 


1 02 


1 09 


1 17 


1 27 




66 


31 


37 


43 


50 


58 


I 05 


1 12 


1 21 


1 31 




67 


33 


38 


45 


53 


i 00 


1 07 


1 16 


1 25 


1 35 




68 


34 


40 


48 


55 


1 02 


1 10 


1 19 


1 30 


1 39 




69 


36 


42 


50 


58 


1 05 


1 13 


1 23 


1 34 


1 4-1 




70 


38 


44 


52 


1 00 


1 08 


1 17 


1 28 


1 39 


1 50 


1 


71 


40 


46 


55 


1 03 


1 12 


1 22 


1 32 


1 44 


1 50 


1 


72 


42 


49 


58 


1 06 


1 16 


1 27 


1 38 


1 50 


2 04 


1 



TABLE or MERIDIONAL PARTS. 



95 



yrros 


1 1- 


r^ 


30 1 40 


50! 60 


70| 83 


90| lOO 


llo| 120| 13C] 








60 


120 


180 


24( 


300 


361 


421 


482 


542 


603 


664 


725 


787 


1 


1 


61 


121 


181 


241 


301 


362 


422 


483 


543 


604 


665 


721 


788 


2 


2 


62 


122 


182 


242 


302 


363 


423 


484 


544 


605 


666 


727 


789 


3 


3 


63 


123 


183 


243 


303 


364 


424 


485 


545 


606 


667 


728 


790 


4 


4 


64 


124 


184 


244 


304 


365 


425 


486 


546 


607 


668 


729 


791 


5 


5 


65 


125 


185 


245 


305 


366 


420 


487 


547 


608 


669 


730 


792 


6 


6 


66 


126 


186 


246 


306 


367 


427 


488 


548 


609 


670 


731 


793 


7 


7 


67 


127 


187 


247 


307 


368 


428 


489 


549 


610 


671 


732 


794, 


8 


8 


68 


128 


188 


248 


308 


369 


429 


490 


550 


611 


672 


734 


795 


9 


9 


69 


129 


189 


249 


309 


370 


430 


491 


551 


612 


673 


735 


796 


10 


10 


70 


130 


190 


250 


310 


371 


431 


492 


552 


613 


664 


736 


797 


11 


11 


71 


131 


191 


251 


311 


372 


432 


493 


553 


614 


675 


737 


798 


12 


12 


72 


132 


192 


252 


312 


373 


433 


494 


554 


615 


676 


738 


799 


13 


13 


73 


133 


193 


253 


313 


374 


434 


495 


555 


616 


677 


739 


800 


14 


14 


74 


134 


194 


254 


314 


375 


435 


496 


556 


617 


678 


740 


801 


15 


15 


75 


135 


195 


255 


315 


376 


436 


497 


557 


618 


679 


741 


802 


16 


16 


76 


136 


196 


256 


316 


377 


437 


498 


558 


619 


680 


742 


803 


17 


17 


77 


137 


197 


257 


317 


378 


438 


499 


559 


620 


681 


743 


804 


18 


18 


78 


138 


198 


258 


318 


379 


439 


500 


560 


621 


682 


744 


805 


19 


19 


79 


139 


199 


259 


319 


380 


440 


501 


561 


622 


683 


745 


806 


20 


20 


80 


140 


200 


260 


320 


381 


441 


502 


562 


623 


684 


746 


807 


21 


21 


81 


141 


201 


261 


321 


382 


442 


503 


563 


624 


685 


747 


808 


22 


22 


82 


142 


202 


262 


322 


383 


443 


504 


564 


625 


687 


748 


809 


23 


23 


83 


143 


203 


263 


323 


384 


444 


505 


565 


626 


688 


749 


810 


24 


24 


84 


144 


204 


264 


324 


385 


445 


506 


567 


627 


689 


750 


811 


25 


25 


85 


145 


205 


265 


325 


386 


446 


507 


568 


628 


690 


751 


812 


26 


26 


86 


146 


206 


266 


326 


387 


447 


508 


569 


629 


691 


752 


813 


27 


27 


87 


147 


207 


267 


327 


388 


448 


509 


570 


631 


692 


753 


815 


28 


28 


88 


148 


208 


268 


328 


389 


449 


510 


571 


632 


693 


754 


816 


29 


29 


89 


149 


209 


269 


330 


390 


450 


511 


572 


633 


694 


755 


81? 


30 


30 


90 


150 


210 


270 


331 


391 


451 


512 


573 


634 


695 


756 


818 


31 


31 


91 


151 


211 


271 


332 


392 


452 


513 


574 


635 


696 


757 


819 


32 


32 


92 


152 


212 


272 


333 


393 


453 


514 


575 


636 


697 


758 


820 


33 


33 


93 


153 


213 


273 


334 


394 


454 


515 


576 


637 


698 


75y 


821 


34 


34 


94 


154 


214 


274 


335 


395 


455 


516 


577 


638 


699 


760 


822 


35 


35 


95 


155 


215 


275 


336 


396 


456 


517 


578 


639 


700 


761 


823 


36 


36 


96 


156 


216 


276 


337 


397 


457 


518 


579 


640 


701 


762 


824 


37 


37 


97 


157 


217 


277 


338 


398 


458 


519 


580 


641 


702 


763 


825 


38 


38 


98 


158 


218 


278 


339 


399 


459 


520 


581 


642 


703 


764 


826 


39 


39 


99 


159 


219 


279 


340 


400 


460 


521 


582 


643 


704 


765 


827 


40 


40 


100 


160 


220 


280 


341 


401 


461 


522 


583 


644 


705 


766 


82S 


41 


41 


101 


161 


221 


281 


342 


402 


462 


523 


584 


645 


706 


767 


829 


42 


4-2 


102 


162 


222 


282 


343 


403 


463 


524 


585 


646 


707 


768 


830 


43 


43 


103 


163 


223 


283 


344 


404 


464 


525 


586 


647 


708 


769 


831 


44 


44 


104 


164 


224 


284 


345 


405 


465 


526 


587 


648 


709 


770 


832 


45 


45 


105 


165 


225 


285 


346 


406 


466 


527 


588 


649 


710 


77 i 


833 


46 


46 


106 


166 


226 


286 


347 


407 


467 


528 


589 


650 


711 


772 


834 


47 


47 


107 


167 


227 


287 


348 


408 


468 


529 


590 


651 


712 


773 


835 


48 


48 


108 


168 


228 


288 


349 


409 


469 


530 


591 


652 


713 


774 


836 


49 


49 


109 


169 


229 


289 


350 


410 


470 


531 


592 


653 


714 


775 


837 


50 


50 


110 


170 


230 


290 


351 


411 


471 


532 


593 


654 


715 


777 


838 


51 


51 


111 


171 


231 


291 


352 


412 


472 


533 


594 


655 


716 


778 


839 


52 


52 


112 


172 


232 


292 


353 


413 


473 


534 


595 


656 


717 


779 


840 


53 


53 


113 


173 


233 


293 


354 


414 


474 


535 


596 


657 


718 


780 


841 


54 


54 


114 


174 


234 


294 


355 


415 


476 


536 


597 


658 


719 


781 


842 


55 


55 


115 


175 


235 


295 


356 


416 


477 


537 


598 


659 


720 


782 


843 


56 


56 


116 


176 


236 


296 


357 


417 


478 


538 


599 


660 


721 


783 


844 


57 


57 


117 


177 


237 


297 


358 


418 


479 


539 


600 


661 


722 


784 


845 


58 


58 


118 


178 


238 


298 


359 


419 


480 


540 


601 


662 


723 


785 


846 


59 


59 


119 


179 


239 


299 


360 


420 


481 


541 


602 


663 


724 


786 


847 



96 








TABLE 


OF MERIDIONAL PARTS. 










M. 1 140| 150| 160| 170| 180| ]90| 20O| 2lo| 220| 230| 24o 


250| 260| 270 





848 


910 


973 


1035 1098 


1161 


1225 1289 


1354 


1419 


1484 


1550;iG16|1684 


1 


850 


911 


974 


36 


99 


63 


26 


90 


55 


20 


85 


51 


18 


85 


2 


851 


913 


975 


37 


1100 


64 


27 


91 


56 


21 


86 


52 


19 


86 


3 


852 


914 


976 


38 


01 


65 


28 


92 


57 


22 


87 


53 


20 


87 


4 


853 


915 


977 


39 


02 


66 


29 


93 


58 


23 


88 


54 


21 


88 


5 


854 


916 


978 


41 


03 


67 


30 


95 


59 


24 


90 


56 


22 


89 


6 


855 


917 


979 


42 


05 


68 


32 


96 


60 


25 


91 


57 


2-3 


90 


7 


856 


918 


980 


43 


06 


69 


33 


97 


61 


26 


92 


58 


24 


91 


8 


857 


919 


981 


44 


07 


70 


34 


98 


62 


27 


93 


59 


25 


93 


9 


858 


920 


982 


45 


08 


71 


35 


99 


63 


28 


94 


60 


28 


94 


10 


859 


921 


983 


1046 


1109 


1172 


1236 


1300 


1364 


1430 


1495 


1561 


1628 


1695 


11 


860 


922 


984 


47 


10 


73 


37 


01 


66 


31 


96 


62 


29 


96 


12 


861 


923 


985 


48 


11 


74 


38 


02 


67 


32 


97 


63 


30 


97 


13 


862 


924 


986 


49 


12 


75 


39 


03 


68 


33 


98 


64 


31 


98 


14 


863 


925 


987 


50 


13 


76 


40 


04 


69 


34 


99 


65 


32 


99 


15 


864 


926 


988 


51 


14 


77 


41 


05 


70 


35 


1500 


67 


33 


1700 


16 


865 


927 


989 


52 


15 


78 


42 


06 


71 


36 


02 


68 


34 


01 


17 


866 


928 


990 


53 


16 


79 


43 


07 


72 


37 


03 


69 


35 


03 


18 


867 


929 


991 


54 


17 


81 


44 


08 


73 


38 


04 


70 


37 


04 


19 


868 


930 


993 


55 


18 


82 


45 


10 


74 


39 


05 


71 


38 


05 


20 


869 


931 


994 


1056 


1119 


1183 


1246 


1311 


1375 


1440 


1506 


1572 


1639 


1706 


21 


870 


932 


995 


57 


20 


84 


48 


12 


76 


41 


07 


73 


40 


07 


22 


871 


933 


996 


58 


21 


85 


49 


13 


77 


43 


OS 


74 


41 


08 


23 


872 


934 


997 


59 


22 


86 


50 


14 


79 


44 


09 


75 


42 


09 


24 


873 


935 


998 


60 


23 


87 


51 


15 


80 


45 


10 


77 


43 


11 


25 


874 


936 


999 


61 


25 


88 


52 


16 


81 


46 


11 


78 


44 


12 


26 


875 


937 


1000 


63 


26 


89 


53 


17 


82 


47 


13 


79 


45 


13 


27 


876 


938 


!001 


64 


27 


90 


54 


18 


83 


48 


14 


80 


47 


14 


28 


877 


939 


1002 


65 


28 


91 


55 


19 


84 


49 


15 


81 


48 


15 


29 


878 


941 


1003 


66 


29 


92 


56 


20 


85 


50 


16 


82 


49 


16 


30 


879 


942 


1004 


1067 


1130 


1193 


1257 


1321 


1386 


1451 


1517 


1583 


1650 


1717 


3i 


880 


943 


05 


68 


31 


94 


58 


22 


87 


52 


18 


84 


51 


18 


32 


882 


944 


06 


69 


32 


95 


59 


24 


88 


53 


19 


85 


52 


20 


33 


883 


945 


07 


70 


33 


96 


60 


25 


89 


55 


20 


86 


53 


21 


34 


884 


946 


08 


71 


34 


98 


61 


26 


90 


56 


21 


88 


54 


22 


35 


885 


947 


09 


72 


35 


99 


62 


27 


92 


57 


22 


89 


56 


23 


36 


886 


948 


10 


73 


36 


1200 


64 


28 


93 


58 


24 


90 


57 


24 


37 


887 


949 


11 


74 


37 


01 


65 


29 


94 


59 


25 


91 


58 


25 


38 


888 


950 


12 


75 


38 


02 


66 


30 


95 


60 


26 


92 


59 


26 


39 


889 


951 


13 


76 


39 


03 


67 


31 


96 


61 


27 


93 


60 


27 


40 


890 


952 


1014 


1077 


1140 


1204 


1268 


1332 


1397 


1462 


1528 


1594 


1661 


1729 


41 


891 


953 


15 


78 


41 


05 


69 


33 


98 


63 


29 


96 


62 


30 


42 


892 


954 


16 


79 


42 


06 


70 


34 


99 


64 


30 


97 


63 


31 


43 


893 


955 


18 


80 


44 


07 


71 


35 


1400 


65 


31 


98 


64 


32 


44 


894 


956 


19 


81 


45 


08 


72 


36 


01 


67 


32 


99 


66 


33 


45 


895 


957 


20 


82 


46 


09 


73 


38 


02 


68 


33 


1600 


67 


34 


46 


896 


958 


21 


84 


47 


10 


74 


39 


03 


69 


35 


01 


68 


35 


47 


897 


959 


22 


85 


48 


11 


75 


40 


05 


70 


36 


02 


69 


36 


48 


898 


960 


23 


86 


49 


12 


76 


41 


06 


71 


37 


03 


70 


38 


49 


899 


961 


24 


87 


50 


13 


77 


42 


07 


72 


38 


04 


71 


39 


50 


900 


962 


1025 


1088 


1151 


1215 


1278 


1343 


1408 


1473 


1539 


1605 


1672 


1740 


51 


901 


963 


26 


89 


52 


16 


80 


44 


09 


74 


40 


06 


73 


41 


52 


902 


964 


27 


90 


53 


17 


81 


45 


10 


75 


41 


08 


75 


42 


53 


903 


965 


28 


91 


54 


18 


82 


46 


11 


76 


42 


09 


76 


43 


54i 904 


966 


29 


92 


55 


19 


83 


47 


12 


77 


43 


10 


77 


44 


55 


905 


968 


30 


93 


56 


20 


84 


48 


13 


79 


44 


11 


78 


46 


56 


90G 


969 


31 


94 


57 


21 


85 


49 


14 


80 


46 


12 


79 


47 


57 


907 


970 


32 


95 


58 


22 


86 


50 


15 


81 


47| 13 


80 


48 


58 


908 


971 


33 


96 


59 


23 


87 


52 


16 


82 


481 14 


81 


49 


59i 909] 972 


34 


97 


601 24 


88 


53 


18 


83i 49 1 15 


82i 50 



TABLE OF MERIDIONAL PARTS. 



97 



M.| 280| 290| 30o| Sio] 320| 330| 34o| 350| 36o| 370| 380| 


39o| 40O| 41o| 




Oi 


7511 


1819 


1888 


1958 


>028 


2100 


2171 


2244 23181 


2393 


2468 


2545 2623 2r02| 




1 ^-\ 


21 


90 


59 


30 


01 


73 


46 19 


94 


70 


46 


24 03 




21 


53 


22 


91 


60 


31 


02 


74 


47 


20 


95 


71 


48 


25j 04 




3 


55 


23 


92 


62 


32 


03 


75 


48 


22 


96 


72 


49 


27 


06 




4 


56 


24 


93 


63 


33 


04 


76 


49 


23 


98 


73 


50 


28 


07 




5 


57 


25 


94 


64 


34 


05 


78 


50 


24 


99 


75 


51 


29 


OS 




6 


58 


26 


95 


65 


35 


07 


79 


52 


25 


2400 


76 


53 


31 


10 




7 


59 


27 


96 


66 


37 


OS 


80 


53 


27 


01 


77 


54 


32 


11 




8 


60 


29 


98 


67 


38 


09 


81 


54 


28 


03 


78 


55 


33 


12 




9 


61 


30 


99 


69 


39 


10 


82 


55 


29 


04 


80 


57 


34 


14 




10 


1762 


1831 


1900 


1970 


2040 


2111 


2184 


2257 2330 1 


2405 


2481 


2558 


2636 


2715 




11 


64 


32 


01 


71 


41 


13 


85 


58 


32 


06 


82 


59 


37 


16 




12 


65 


33 


02 


72 


43 


14 


86 


59 


33 


08 


84 


60 


38 


18 




13 


66 


34 


03 


73 


44 


15 


87 


60 


34 


09 


85 


62 


40 


19 




14 


67 


35 


05 


74 


45 


16 


88 


61 


35 


10 


86 


63 


41 


20 




15 


68 


37 


06 


76 


46 


17 


90 


63 


37 


11 


87 


64 


42 


22 




16 


69 


38 


07 


77 


47 


19 


91 


64 


38 


13 


89 


66 


44 


23 




17 


70 


39 


08 


78 


48 


20 


92 


65 


39 


14 


90 


67 


45 


24 




18 


72 


40 


09 


79 


50 


21 


93 


66 


40 


15 


91 


68 


46 


26 




19 


73 


41 


10 


80 


51 


22 


94 


68 


42 


16 


92 


69 


48 


27 




20 


1774 


1842 


1912 


1981 


2052 


2123 


2196 


2269 


2343 


2418 


2494 


2571 


2649 


2728 




21 


75 


43 


13 


83 


53 


25 


97 


70 


44 


19 


95 


72 


50 


29 




22 


76 


45 


14 


84 


54 


26 


98 


71 


45 


20 


96 


73 


51 


'31 




23 


77 


46 


15 


85 


56 


27 


99 


72 


46 


22 


98 


75 


53 


32 




24 


78 


47 


16 


86 


57 


28 


2200 


74 


48 


23 


99 


76 


54 


33 




25 


80 


48 


17 


87 


58 


29 


02 


75 


49 


24 


2500 


77 


.-■S5 


35 




26 


81 


49 


18 


88 


59 


31 


03 


76 


50 


25 


01 


.-78 


57 


36 




27 


82 


50 


20 


90 


60 


32 


04 


77 


51 


27 


03 


80 


58 


37 




28 


83 


52 


21 


91 


61 


33 


05 


79 


53 


28 


,04 


81 


59 


39 




29 


84 


53 


22 


92 


63 


34 


07 


80 


54 


29 


'05 


82 


61 


40 




30 


1785 


1854 


1923 


1993 


2064 


2135 


2208 


2281 


2355 


2430 


2506 


2584 


2662 


2742 




31 


86 


55 


24 


94 


65 


37 


0. 


82 


56 


. 32 


08 


85 


63 


43 




32 


87 


56 


25 


95 


66 


38 


10 


83 


.58 


33 


09 


86 


65 


4.4 




33 


89 


57 


27 


97 


67 


39 


11 


85 


■59 


34 


10 


88 


66 


46 




34 


90 


58 


28 


98 


69 


40 


13 


86 


60 


35 


12 


89 


67 


47 




35 


91 


60 


29 


99 


70 


41 


14 


87 


61 


37 


13 


90 


69 


48 




36 


92 


61 


30 


2000 


71 


43 


15 


^.88 


63 


38 


14 


91 


70 


50 




37 


93 


62 


31 


01 


72 


44 


1^ 


90 


64 


39 


15 


93 


71 


51 




38 


94 


63 


32 


02 


73 


45 


17 


91 


65 


40 


17 


94 


73 


52 




39 


95 


64 


34 


04 


75 


46 


19 


92 


66 


42 


18 


95 


74 


54 




40 


1797 


1865 


1935 


2005 


2076 


.147 


2220 


2293 


£368 


2443 


2519 


2597 


2675 


2755 




41 


98 


66 


36 


06 


77 


49 


21 


95 


69 


44 


21 


98 


76 


56 




42 


99 


68 


37 


07 


78 


50 


22 


96 


70 


45 


22 


99 


78 


58 




43 


1800 


69 


38 


08 


79 


51 


24 


97 


71 


47 


23 


2600 


79 


59 




44 


01 


70 


39 


10 


80 


52 


25 


98 


73 


48 


24 


02 


80 


60 




45 


02 


71 


41 


11 


82 


53 


26 


99 


74 


49 


26 


03 


82 


62 




46 


03 


72 


42 


12 


83 


55 


27 


2301 


75 


51 


27 


04 


83 


63 




47 


05 


73 


43 


13 


84 


56 


28 


02 


76 


52 


28 


06 


84 


64 




48 


06 


75 


44 


14 


85 


57 


30 


03 


78 


53 


30 


07 


86 


66 




49 


07 


76 


45 


15 


86 


58 


31 


04 


79 


54 


31 


08 


87 


67 




50 


1808 


1877 


1946 


2017 


2088 


2159 


2232 


2306 


2380 


2456 


2532 


2610 


2688 


2768 




51 


09 


78 


48 


18 


89 


61 


33 


07 


81 


57 


33 


11 


90 


70 




52 


10 


79 


49 


19 


90 


62 


35 


08 


83 


58 


35 


12 


91 


71 




53 


11 


80 


50 


20 


91 


63 


36 


09 


84 


59 


36 


14 


92 


72 




54 


13 


81 


51 


21 


92 


64 


37 


11 


85 


61 


37 


15 


94 


74 




55 


14 


83 


52 


22 


94 


65] 38 


12 


86 


62 


38 


16 


95 


75 




56 


15 


84 


53 


24 


95 


67 39 


13 


88 


63 


4C 


17 


96 


76 




57 


16 


85 


55 


25 


96 


68 41 


14 


89 


64 


41 


19 


98 


78 




58 


17 


86 


50 


26 


97 


69 42 


16 


9C 


66 


4S 


2C 


9S 


79 




59 


18 


S7 


fi7j 27 


98| 70i 43 


17 


91 


6' 


441 21 


270C 


80 





98 



TABLE OF MERIDIONAL PARTS. 



M.|420|430|440| 450 


46o| 470| 480I 49-3| 5i)-3 


-5"lo 


520 


530 


■540 


550! 





2782 286312946 


30)0 


3116 


3203 


329213382:3474 


3569 


3665 


3764|33G5;39fi8 | 


1 


83 


64 


47 


31 


17 


04 


9'.^l 84! 76 


70 


67 


65 


67 


70 


2 


84 


66 


49 


33 


18 


06 


■ 95] 85 


78 


72 


68 


67 


68 


71 


3 


86 


67 


50 


34 


20 


07 


96 


87 


79 


74 


70 


69 


70 


73 


4 


87 


69 


51 


36 


21 


09 


98 


88 


81 


75 


72 


70 


71 


75 


5 


88 


70 


53 


37 


23 


10 


99 


90 


82 


77 


73 


72 


73 


77 


6 


90 


71 


54 


38 


24 


12 


3301 


91 


84 


78 


75 


71 


75 


78 


? 


91 


73 


56 


40 


26 


13 


02 


93 


85 


80 


77 


75 


77 


80 


8 


92 


74 


57 


41 


27 


14 


03 


94 


87 


82 


78 


77 


78 


82 


9 


94 


75 


58 


43 


29 


16 


05 


96 


88 


83 


80 


79 


80 


84 


10 


2795 


2877 


2960 


3044 


3130 


3217 


3306 


3397 


3490 


3585 


3681 


3780 


3882 


3985 


11 


97 


78 


61 


46 


31 


19 


08 


99 


92 


86 


83 


82 


83 


87 


!2 


98 


80 


63 


47 


33 


20 


09 


3400 


93 


88 


85 


84 


85 


89 


13 


99 


81 


64 


48 


34 


22 


11 


02 


95 


90 


86 


85 


87 


91 


14 


2801 


82 


65 


5U 


36 


23 


12 


03 


96 


91 


88 


87 


89 


92 


]5 


02 


84 


67 


51 


37 


25 


14 


05 


98 


93 


90 


89 


90 


94 


16 


03 


85 


68 


53 


39 


26 


16 


07 


99 


94 


91 


90 


92 


96 


17 


05 


86 


70 


54 


40 


28 


17 


08 


3501 


96 


93 


92 


94 


98 


18 


06 


88 


71 


55 


42 


29 


19 


10 


03 


98 


95 


94 


95 


99 


19 


07 


89 


72 


57 


43 


31 


20 


11 


04 


99 


96 


95 


97 


4001 


20 


2809 


2891 


2974 


3058 


3144 


3232 


3322 


3413 


350G 


3601 


3598 


3797 


3899 


40O3 


21 


10 


92 


75 


60 


46 


34 


24 


14 


07 


02 


99 


99 


M-i\ 


05 


22 


11 


93 


76 


61 


47 


35 


25 


16 


09 


04 


3701 


3800 


02 


06 


23 


13 


95 


78 


63 


49 


37 


26 


17 


10 


06 


03 


02 


04 


08 


24 


14 


96 


79 


64 


50 


38 


28 


19 


12 


07 


04 


04 


06 


10 


25 


15 


97 


81 


65 


52 


40 


29 


20 


14 


09 


06 


or-, 


07 


12 


2f) 


17 


99 


82 


67 


53 


41 


31 


22 


15 


10 


07 


07 


09 


14 


27 


18 


2900 


83 


6S 


55 


42 


32 


23 


17 


12 


09 


09 


11 


15 


28 


20 


02 


85 


70 


56 


44 


34 


25 


18 


14 


11 


11 


13 


17 


29 


21 


03 


86 


71 


57 


45 


35 


27 


20 


15 


13 


12 


14 


19 


30 


2822 


2904 


2988 


3073 


3159 


3247 


3337 


3428 


3521 


3617 


3714 


3814 


3916 


4021 


31 


24 


06 


89 


74 


60 


48 


38 


30 


23 


18 


16 


16 


18 


22 


32 


25 


07 


91 


75 


62 


50 


40 


31 


25 


20 


17 


17 


19 


24 


33 


26 


08 


92 


77 


63 


51 


41 


33 


26 


22 


19 


19 


21 


28 


34 


28 


10 


93 


78 


65 


53 


43 


34 


28 


23 


21 


21 


22 


28. 


35 


29 


11 


95 


80 


66 


54 


44 


36 


29 


25 


22 


22 


25 


29 


36 


30 


13 


96 


81 


68 


50 


46 


37 


31 


26 


•24 


24 


26 


31 


37 


32 


14 


98 


83 


69 


57 


47 


39 


32 


28 


26 


26 


28 


33 


38 


33 


15 


99 


84 


71 


59 


49 


40 


34 


30 


27 


27 


30 


35 


39 


34 


17 


3000 


85 


72 


60 


50 


42 


36 


31 


29 


29 


32 


37 


40 


2836 


2918 


3002 


3087 


3173 


3262 


3352 


3443 


3537 


3633 


3731 


3 31 


3933 


4038 


41 


37 


19 


03 


88 


75 


63 


53 


45 


39 


34 


32 


32 


35 


40 


42 


39 


21 


05 


90 


76 


65 


55 


47 


40 


36 


34 


34 


37 


42 


43 


40 


22 


06 


91 


78 


66 


56 


48 


42 


38 


36 


36 


38 


44 


44 


41 


24 


07 


93 


79 


68 


58 


50 


43 


39 


37 


3S 


40 


45 


45 


43 


25 


09 


94 


81 


69 


59 


51 


45 


41 


39 


39 


42 


47 


46 


44 


26 


10 


95 


82 


71 


61 


53 


47 


43 


41 


41 


44 


49 


47 


45 


28 


12 


97 


84 


72 


62 


54 


48 


44 


42 


43 


45 


51 


48 


47 


29 


13 


98 


85 


74 


64 


56 


50 


46 


44 


44 


47 


52 


49 


48 


31 


14 


3100 


87 


75 


65 


57 


51 


47 


46 


46 


49 


54 


50 


2849 


2932 


3016 


3101 


3188 


3277 


3367 


3459 


3553 


3649 


3747 


3848 


3951 


4056 


51 


51 


33 


17 


03 


90 


78 


68 


60 


55 


51 


49 


49 


52 


58 


52 


52 


35 


19 


04 


91 


80 


70 


62 


56 


52 


50 


51 


54 


60 


53 


54 


36 


20 


05 


92 


81 


71 


64 


58 


54 


52 


53 


56 


61 


54 


55 


37 


21 


07 


94 


83 


73 


65 


59 


55 


54 


54 


58 


63 


55 


56 


39 


23 


08 


95 


84 


74 


67 


61 


57 


55 


56 


59 


65 


56 


58 


40 


24 


10 


97 


86 


76 


68 


62 


59 


57 


58 


61 


67 


57 


59 


42 


26 


11 


98 


87 


78 


70 


64 


60 


59 


60 


63 


69 


58 


60 


43 


27 


13i3200 


89 


79 


71 


66 


62 


60 


61 


64 


70 


59 


62 


44 29' I4I 01 


90 


«1 


73 1 67' 64 


62 


fi:^ 


66 


72 



TABLE OF MERIDIONAL PARTS. 



99 



M. 


560 


570 


58^1 590 


60O| 61o| 620| 630| 640| 65o| 66o| 670| 680, (i.^jcj 


4074 4183 429414409 


452T 


4649 477514905 5039 5179,5324 


5474 5631 5795 | 


1 76 


84 


96 


11 


29 


51 


77 07 


42 81 


26 


77 


33 97 


2 77 


86 


98 


13 


31 


53 


79 


09 


44 84 


28 


79 


36 5800 


3 '/9 


88 


4300 


15 


33 


55 


81 


12 


46 86 


31 


82 


39 


03 


4 81 


90 


02 


17 


35 


57 


84 


14 


49 88 


33 


84 


42 


06 


5 83 


92 


04 


19 


37 


60 


86 


16 


51: 91 


36 


87 


44 


09 


6 85 


94 


06 


21 


39 


62 


88 


18 


53 93 


38 


89 


47 


li 


7 86 


95 


08 


23 


41 


64 


90 


20 


55 95 


41 


92 


50 


14 


8 88 


97 


09 


25 


43 


66 


92 


23 


58 98 


43 


95 


52 


17 


9 90 


99 


11 


27 


45 


68 


94 


25 


60 5200 


46 


97 


55 


20 


10 4092 


4201 


4313 


4429 


4547 


4670 


4796 


4927 


5062 5303 


5348 


5500 


5658 


5823 


11 


94 


03 


15 


31 


49 


72 


98 


29 


65 05 


51 


02 


60 


25 


12 


95 


05 


17 


33 


51 


74 


4801 


31 


67 


07 


53 


05 


63 


28 


13 


97 


07 


19 


34 


53 


76 


03 


34 


69 


10 


56 


07 


66 


31 


14' 99 


OS 


21 


36 


55 


78 


05 


36 


71 


.12 


58 


10 


68 


34 


15 4101 


10 


23 


38 


57 


80 


07 


38 


74 


14 


61 


13 


71 


37 


16 


03 


12 


25 


40 


59 


82 


09 


40 


76 


17 


63 


15 


74 


39 


17 


04 


14 


27 


42 


62 


84 


11 


43 


78 


19 


66 


18 


76 


42 


18 


05 


16 


28 


44 


64 


87 


14 


45 


81 


22 


68 


20 


79 


45 


19 


08 


18 


30 


46 


66 


89 


16 


47 


83 


24 


71 


23 


82 


48 


20 


4110 


4220 


4332 


4448 


4568 


4691 


4818 


4949 


5085 


5226 


5373 


5526 


5085 


5851 


21 


12 


21 


34 


50 


70 


93 


20 


51 


88 


29 


76 


28 


87 


54 


22 


13 


23 


36 


52 


72 


95 


22 


54 


90 


31 


78 


31 


90 


56 


23 


15 


25 


38 


54 


74 


97 


24 


56 


92 


34 


80 


33 


93 


59 


24 


17 


27 


40 


56 


76 


99 


26 


58 


95 


36 


83 


36 


95 


02 


25 


19 


29 


42 


58 


78 


4701 


29 


60 


97 


38 


85 


39 


98 


65 


26 


21 


31 


44 


60 


80 


03 


31 


63 


99 


41 


88 


41 


5701 


68 


27 


22 


32 


46 


62 


82 


05 


33 


65 


5102 


43 


90 


44 


04 


71 


28 


24 


34 


47 


64 


84 


07 


35 


67 


04 


46 


93 


46 


06 


74 


29 


26 


36 


49 


66 


86 


10 


37 


69 


06 


48 


95 


49 


09 


76 


30 


4128 


423S 


4351 


4468 


4588 


4712 


4839 


4972 


5108 


5250 


5398 


5552 


5712 


5879 


31 


30 


40 


53 


70 


90 


14 


42 


74 


11 


53 


>401 


54 


15 


82 


32 


32 


42 


55 


72 


92 


16 


44 


76 


13 


55 


03 


57 


17 


85 


33 


33 


44 


57 


74 


94 


18 


46 


78 


15 


58 


06 


59 


20 


88 


34 


35 


46 


59 


76 


96 


20 


48 


81 


18 


60 


08 


62 


23 


91 


35 


37 


47 


61 


78 


98 


22 


50 


83 


20 


63 


11 


65 


25 


94 


36 


39 


49 


63 


80 


4600 


24 


52 


85 


22 


65 


13 


67 


28 


96 


37 


41 


51 


65 


82 


02 


26 


55 


87 


25 


67 


16 


70 


31 


99 


38 


42 


53 


67 


84 


04 


28 


57 


90 


27 


70 


18 


73 


34 


5902 


39 


44 


55 


69 


86 


06 


31 


59 


92 


29 


72 


21 


75 


36 


05 


40 


4146 


4257 


4370 


4488 


4608 


4733 


4861 


i994 


5132 


5275 


5423 


5578 


5739 


5908 


41 


48 


59 


72 


90 


10 


35 


63 


96 


34 


77 


26 


80 


42 


11 


42 


50 


60 


74 


92 


12 


37 


65 


99 


36 


80 


28 


83 


45 


14 


43 


52 


62 


76 


94 


14 


39 


68 


5001 


39 


82 


31 


86 


47 


17 


44 


53 


64 


78 


95 


16 


41 


70 


03 


41 


84 


33 


88 


50 


19 


45 


55 


66 


80 


97 


18 


43 


72 


05 


43 


87 


36 


91 


53 


22 


46 


57 


68 


82 


99 


20 


45 


74 


08 


46 


89 


38 


94 


56 


25 


47 


59 


70 


84 


4501 


23 


47 


76 


10 


48 


92 


41 


96 


58 


28 


48 


61 


72 


86 


03 


25 


50 


79 


12 


51 


94 


43 


99 


61 


31 


49 


62 


74 


88 


05 


27 


52 


81 


14 


53 


97 


46 


5602 


64 


34 


50 


4164 


4275 


4390 


4507 


4629 


4754 


4883 


5017 


5155 


5299 


5448 


5604 


5767 


5937 


51 


66 


77 


92 


09 


31 


56 


85 


19 


58 


5301 


51 


07 


70 


40 


52 


08 


79 


94 


11 


33 


58 


87 


21 


60 


04 


54 


10 


72 


43 


53 


70 


81 


96 


13 


35 


60 


90 


23 


62 


06 


56 


12 


75 


46 


54 


72 


83 


98 


15 


37 


62 


92 


26 


65 


09 


59 


15 


78 


48 


55 


73 


85 


99 


17 


39 


64 


94 


28 


67 


11 


61 


17 


81 


51 


56 


75 


87 


4401 


19 


41 


66 


96 


30 


69 


14 


64 


20 


83 


54 


57 


77 


89 


03 


21 


43 


69 


98 


33 


72 


16 


66 


23 


86 


57 


58 


79 


91 


05 


23 


45 


7114901 


35 


74 


19 


69 


25 


89 


60 


59 


81 


92 


07 


25 


47 


73 i 03 


37 


76' 21 


71' 28 


92 


6Z 



100 






TABLE 


OF M 


ERIDIONAL PARTS 










M. 


70O| 710| 720| 730| 740( 750| 760| 770| 780| 790] 80O| 8io| 820l 8:)o\ 


015366 6146i6335 6534 


6746 


6970 


7210 


7467 


7745 8046] 8375 


8739 0145 


9606 


1 


65: 49 


38 


38 


49 


74 


14 


72 


49 


51 


81 


45 


53 


14 


2 


73 


52 


41 


41 


53 


78 


18 


76 


54 


56 


87 


52 


60 


22 


3 


75 


55 


45 


45 


57 


82 


22 


81 


59 


61 


93 


58 


67 


31 


4 


78 


58 


48 


48 


60 


86 


27 


85 


64 


67 


98 


65 


74 


39 


5 


81 


61 


51 


52 


64 


90 


31 


90 


69 


72 


8404 


71 


82 


47 


6 


84 


64 


54 


55 


68 


94 


35 


94 


74 


77 


10 


78 


89 


55 


7 


86 


67 


58 


58 


71 


97 


39 


98 


78 


83 


16 


84 


96 


64 


8 


89 


70 


61 


62 


75 


7001 


43 


7503 


83 


88 


22 


91 


9203 


72 


9 


92 


73 


64 


65 


79 


05 


47 


07 


88 


93 


27 


97 


11 


81 


10 


5995 


6177 


6367 


6569 


6782 


7009 


7252 


7512 


7793 


8099 


8433 


8804 


9218 


9689 


11 


98 


80 


71 


72 


86 


13 


56 


16 


98 


8104 


39 


10 


25 


97 


12 


6001 


83 


74 


76 


90 


17 


60 


21 


7803 


09 


45 


17 


33 


9706 


13 


04 


86 


77 


79 


93 


21 


64 


25 


OS 


15 


51 


23 


40 


14 


14 


07 


89 


80 


83 


97 


25 


68 


30 


13 


20 


57 


30 


48 


23 


15 


10 


92 


84 


86 


6801 


29 


73 


35 


17 


25 


63 


36 


55 


31 


16 


13 


95 


87 


90 


04 


33 


77 


39 


22 


31 


69 


43 


62 


40 


17 


16 


98 


90 


93 


08 


37 


81 


44 


27 


36 


74 


49 


70 


48 


18 


19 


6201 


94 


96 


12 


41 


85 


48 


32 


41 


80 


56 


77 


57 


19 


22 


05 


97 


6600 


15 


45 


89 


53 


37 


47 


86 


63 


85 


65 


20 


6025 


6208 


6400 


0603 


6S19 


7049 


7294 


7557 


7842 


8152 


8492 


8869 


9292 


9774 


21 


28 


11 


03 


07 


23 


52 


98 


62 


47 


58 


98 


76 


9300 


83 


22 


31 


14 


07 


10 


26 


56 


7302 


66 


52 


63 


8504 


83 


07 


91 


23 


34 


17 


10 


14 


30 


60 


06 


71 


57 


68 


10 


89 


15 


9800 


24 


37 


20 


13 


17 


34 


64 


11 


76 


62 


74 


16 


96 


22 


09 


25 


40 


23 


17 


21 


38 


68 


15 


80 


67 


79 


22 


8903 


30 


17 


26 


43 


26 


20 


24 


41 


72 


19 


85 


72 


85 


28 


09 


38 


26 


27 


46 


30 


23 


28 


45 


76 


23 


89 


77 


90 


34 


16 


45 


35 


28 


49 


33 


27 


31 


49 


80 


28 


94 


82 


96 


40 


23 


53 


44 


29 


52 


36 


30 


35 


53 


84 


32 


98 


87 


8201 


46 


30 


60 


52 


30 


6055 


6239 


6433 


6639 


6856 


7088 


7336 


7603 


7892 


8207 


8552 


8936 


9308 


9861 


31 


58 


42 


37 


42 


60 


92 


40 


08 


97 


12 


58 


43 


76 


70 


32 


61 


45 


40 


46 


64 


96 


45 


12 


7902 


18 


64 


50 


83 


79 


33 


64 


49 


43 


49 


68 


7100 


49 


17 


07 


23 


71 


57 


91 


88 


34 


67 


52 


47 


53 


71 


04 


53 


22 


12 


29 


77 


63 


99 


97 


35 


70 


55 


50 


56 


7-5 


08 


68 


26 


17 


34 


83 


70 


9407 


9906 


30 


73 


58 


53 


60 


79 


12 


62 


31 


22 


40 


89 


77 


14 


15 


37 


76 


61 


57 


63 


83 


16 


66 


36 


27 


45 


95 


84 


22 


24 


38 


79 


64 


60 


67 


8r 


20 


71 


40 


32 


51 


8601 


91 


30 


33 


39 


82 


68 


63 


70 


9C 


24 


75 


45 


37 


56 


07 


98 


3fc 


42 


40 


6085 


6271 


6467 


6674 


0894 


7128 


7379 


7650 


7942 


8262 


8614 


9005 


9445 


9951 


41 


88 


74 


70 


77 


98 


32 


84 


54 


48 


67 


20 


12 


53 


60 


42 


91 


77 


73 


81 


6901 


36 


88 


59 


53 


73 


20 


18 


61 


69 


43 


94 


80 


77 


85 


05 


40 


92 


64 


58 


79 


32 


25 


69 


78 


44 


97 


83 


80 


88 


09 


45 


97 


68 


63 


84 


38 


32 


77 


87 


45 


6100 


87 


83 


92 


13 


49 


7401 


73 


68 


90 


44 


39 


85 


9996 


40 


04 


90 


87 


95 


17 


53 


06 


78 


73 


95 


51 


40 


93 


10005 


47 


00 


93 


90 


99 


20 


57 


10 


83 


78 


8301 


57 


53 


9501 


10015 


4S 


09 


96 


94 


0702 


24 


61 


14 


87 


83 


07 


63 


60 


09 


10024 


49 


12 


99 


97 


06 


28 


65 


19 


92 


89 


12 


69 


67 


17 


10033 


50 


0115 


0303 


6500 


6710 


6932 


7169 


7423 


7697 


7994 


8318 


8676 


9074 


9525 


10043 


51 


IH 


00 


04 


13 


36 


73 


27 


7702 


99 


24 


82 


81 


33 


10052 


52 


21 


09 


07 


17 


40 


77 


32 


06 


8004 


29 


88 


88 


41 


10061 


53 


24 


12 


11 


20 


43 


81 


36 


11 


09 


35 


93 


96 


49 


10071 


54 


27 


15 


14 


24 


47 


85 


41 


16 


14 


41 


8701 


9103 


57 


100«0 


55 


3( 


19 


17 


28 


51 


89 


45 


21 


20 


47 


07 


10 


G5l 10089 


50 


33 


22 


21 


31 


55 


94 


49 


25 


25 


52 


14 


17 


73 10(199 


57 


3( 


25 


24 


35 


59 


98 


54 


30 


30 


58 


20 


24 


8l!l0108 


58 


41 


28 


28 


38 


63 '[7202 


58 


35 


35 


04 


26 


31 


89|l(ll 18 


59 


4; 


32 


31 


42 


66 


1 06 


63 


40 


40 


69 


33 


38 


98 


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I'lale 1 




Plate 1 




Hate 'i 









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Pfcite 




Plate 5. 



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Fl<)us:>lie.l L. 



"Vine yard 



S - ■*. „ 44. 'i i^t 

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-, » «i ^ % % 4 

DETAILS OF LEAVES 



i < S i i ) > 

M 5 $ i V 5 

I I M 1 i i 

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:'Ocik 



fA'^cods 






'"^Kk^^r 



Heath 




m©^ps. &i, 



RPike road 



^\/\/\/VVV"ooden Fence Ay\/y\^- 

_Conujioiiioad_^^___ 



^7W. 



J/r/J/zTi/ /'/"■/,■ 

/',/////>■!/ //!/■ f'l//l/l/i/l 

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/)(>. Saw 

Do. Sua/ii 
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Tri//fii<»iifri'r/i/ /'ri/it 






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PmiOu-tmu Sr XT. 



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Direction of the cuixpnt 



Jtucks souietiuies iiaTe 



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Anihorag-p J^ for Ships 



Huoys 



Rocks .ihcivs * , 
' ("hainiel-^ "niaiks 


— 


n^a 


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Haffjonrs 


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it4icki> soiuetiDies h i 




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